Field arithmetic

Ergebnisse der Mathematik und ihrer Grenzgebiete

Volumn 11, Issue , 2008, Pages 1-768

  Fried, Michael D ^a   Jarden, Moshe ^b  

^a MONTANA STATE UNIVERSITY BILLINGS   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 75249106141     PISSN: 00711136     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article

References (256)

1. S. S. Abhyankar. Coverings of algebraic curves, American Journal of Mathematics 79 (1957), 825-856.
2. A. Adler and C. Kiefe. Pseudo Snite fields, procyclic fields and model completion, Pacific Journal of Mathematics 62 (1976), 305-309.
3. J. Kr. Arason, B. Fein, M. Schacher, and J. Sonn. Cyclic extensions of K(=)/K, Transactions of the American Mathematical Society 313 (1989), 843-851.
4. E. Artin. Über eine neue Art von L-Reihen, Abhandlungen aus dem mathematischen Seminar der Universität Hamburg 3 (1924), 89-108; Collected Papers, Addison-Wesley (1965), 105-124.
5. E. Artin. Beweis des allgemeinen Reziprozitätsgesetzes, Abhandlungen aus dem mathematischen Seminar der Universität Hamburg 5 (1927), 353-363; Collected Papers, Addison-Wesley (1965), 131-141.
6. E. Artin. Algebraic Numbers and Algebraic Functions, Gordon and Breach, New York, 1967.
7. M. Aschbacher and R. Gurlanick. Some applications of the first cohomology group, Journal of Algebra 90 (1984), 446-460.
8. J. Ax. Solving diophantine problems modulo every prime, Annals of Mathematics 85 (1967), 161-183.
9. J. Ax. The elementary theory of finite fields, Annals of Mathematics 88 (1968), 239-271.
10. J. Ax. Fnjective endomorphisms of varieties and schemes, Pacific Journal of Mathematics 31 (1969), 1-7.
11. J. Ax. A mathematical approach to some problems in Number theory, Proceedings of Symposia in Pure Mathematics 20 (1971), 1969 Institute on Number Theory, AMS, 161-190.
12. J. Ax and S. Kochen. Diophantine problems over local fields I, American Journal of Mathematics 87 (1965), 605-630.
13. J. Ax and S. Kochen. Diophantine problems over local fields II, American Journal of Mathematics 87 (1965), 631-648.
14. J. Ax and S. Kochen. Diophantine problems over local fields III, Annals of Mathematics 83 (1966), 437-456.
15. J. L. Bell and A. B. Slomson. Models and ultraproducts: an introduction, North-Holland, Amsterdam, American Elsevier, New York, 1974.
16. E. Binz, J. Neukirch, and G. H. Wenzel. A subgroup theorem for free products of profinite groups, Journal of Algebra 19 (1971), 104-109.
17. M. Bocher. Introduction to Higher Algebra, Macmillan, New York, 1947.
18. E. Bombieri. Counting points on curves over finite fields, (d'apres S. A. Stepanov), Seminaire Bourbaki 1972/1973, Exp. 430, Lecture Notes in Mathematics 383, pp. 234-241, Springer-Verlag, Berlin, 1974.
19. E. Bombieri. On exponential sums in Suite fields II, Inventiones mathematicae 47 (1978), 29-39.
20. Z. I. Borevich and I. R. Shafarevich. Number Theory, Academic Press, New York, 1966.
21. N. Bourbaki. Algebra I, Hermann, Paris, 1974.
22. N. Bourbaki. Commutative Algebra, Chapters 1-7, Springer, Berlin, 1989.
23. A. Brandis. Verschränkte Homomorphismen endlicher Gruppen, Mathematische Zeitschrift 162 (1978), 205-217.
24. D. Brink. On alternating and symmetric groups as Galois groups, Israel Journal of Mathematics (2004).
25. W. Burnside. On simply transitive groups of prime degree, Quarterly Journal of Mathematics 37 (1906), 215-221.
26. W. Burnside. Theory of groups of finite order, 2nd edition, Dover Publications, New York, 1955.
27. J. W. S. Cassels and A. Fröhlich. Algebraic Number Theory, Academic Press, London, 1967.
28. Z. M. Chatzidakis. Model theory of pro Snite groups, Dissertation, Yale University, 1984.
29. Z. M. Chatzidakis. Some properties of the absolute Galois group of a Hilbertian field, Israel Journal of Mathematics 55 (1986), 173-183.
30. Z. M. Chatzidakis. A projective profinite group whose smallest embedding cover is not projective, Israel Journal of Mathematics 85 (1994), 1-9.
31. Z. M. Chatzidakis. Model theory of profinite groups having the Iwasawa property, Illinois Journal of Mathematics 42 (1998), 70-96.
32. G. Cherlin, L. v. d. Dries and A. Macintyre. The elementary theory of regularly closed fields, manuscript, 1980.
33. G. Cherlin and M. Jarden. Undecidability of some elementary theories over PAC fields, Annals of Pure and Applied Logic 30 (1986), 137-163.
34. C. Chevalley. Demonstration d'une hypothése de M. Artin, Abhandlungen aus dem Mathe-matischen Seminar Hamburg 11 (1936), 73-75.
35. C. Chevalley. Introduction to the theory of algebraic functions of one variable, Mathematical Surveys VI, AMS, Providence, 1951.
36. S. D. Cohen and M. Fried. Lenstra's proof of the Carlitz-Wan conjecture on exceptional polynomials: An elementary version. Finite Fields and their Applications 1 (1995), 372-375.
37. P. M. Cohn. Algebra, Vol. 2, 2nd Edition, John Wiley & Sons, Chicoster, 1989.
38. J. -L. Colliot-Thélène. Rational connectedness and Galois covers of the projective line, Annals of Mathematics 151 (2000), 359-373.
39. P. Corvaja and U. Zannier. Values of rational functions on non-Hilbertian fields and a question of Weiss-auer, Israel Journal of Mathematics 105 (1998), 323-335.
40. J. Cossey, O. H. Kegel, and L. G. Kovács. Maximal Frattini extensions, Archiv der Mathematik 35 (1980), 210-217.
41. P. Dèbes. Galois covers with prescribed fibers: the Beckmann-Black Problem, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Serie 6, 28 (1999), 273-286.
42. P. Dèbes and D. Haran. Almost hilbertian fields, Acta Arithmetica 88 (1999), 269-287.
43. P. Deligne. La conjecture de Weil I, IHES Publications Mathematiques 43, (1974), 273-307.
44. J. Denef, M. Jarden, and D. J. Lewis. On Ax-fields which are d, Quarterly Journal of Mathematics Oxford (2) 34 (1983), 21-36.
45. J. Denef and F. Loeser. DeGnable sets, motives and P-adic integrals, Journal of the American Mathematical Society 14 (2001), 429-469.
46. M. Deuring. Über den Tchebotareffschen Dichtigkeitssatz, Mathematische Annalen 110 (1934), 414-415.
47. M. Deuring. Lectures on the Theory of Algebraic Functions of One Variable, Lecture Notes in Mathematics 314, Springer-Verlag, Berlin, 1973.
48. J. D. Dixon. The probability of generating the symmetric group, Mathematische Zeitschrift 110 (1969), 199-205.
49. J. D. Dixon, M. P. F. du Sautoy, A. Mann, and D. Segal. Analytic pro-p Groups, Second Edition, Cambridge Studies in Advanced Mathematics 61, Cambridge University Press, Cambridge, 1999.
50. J. D. Dixon, L. Pyber, A. Seress, and A. Shalev. Residual properties of free groups and probabilistic methods, Journal für die reine und angewandte Mathematik 556 (2003) 159-172.
51. A. Douady. Cohomologie des groupes compacts totalement discontinus, Séminaire Bour-baki 1959-1960, Exposé 189.
52. L. van dan Dries and K. Schmidt. Bounds in the theory of polynomial rings over fields. A nonstandard approach, Inventiones mathematicae 76 (1984), 77-91.
53. L. van dan Dries and R. L. Smith. Decidable regularly closed fields of algebraic numbers, Journal of Symbolic Logic 50 (1985), 468-475.
54. V. G. Drinfeld and S. Vlâdut. Number of points on an algebraic curve, Functional analysis and its applications 17 (1983), 68-69(Russian).
55. J.-L. Duret. Les corps faiblement algébraiquement clos non separablement clos ont la pro-priete d'independence, in Model Theory of Algebra and Arithmetic, Pacholski et. al. editors, Lecture Notes in Mathematics 834 Springer-Verlag, Berlin, 1980.
56. D. Dwork. On the rationality of the zeta function of an algebraic variety, American Journal of Mathematics 82 (1960), 631-648.
57. D. Dwork. On the zeta function of a hypersurface III, Annals of Mathematics 83 (1966), 457-519.
58. I. Efrat. A Hasse principle for function fields over PAC Gelds, Israel Journal of Mathematics 122 (2001), 43-60.
59. M. Eichler. Zum Hilbertschen Irreduzibilitatssatz, Mathematische Annalen 116 (1939), 743-748.
60. Ju. L. Ershov. Fields with a solvable theory, Soviet Mathematics Doklady 8 (1967), 575-576.
61. Ju. L. Ershov. ProSnite groups, Algebra i Logica (Russian) 19 (1980), 552-565; Algebra and Logic (English translation) 19 (1980), 357-366.
62. Ju. L. Ershov. Regularly closed fields, Soviet Mathematics Doklady 31 (1980), 510-512.
63. Ju. L. Ershov. Undecidability of regularly closed fields, Algebra and logic 20 (1981), 257-260.
64. Ju. L. Ershov. A talk in a conference in the theory of models, Oberwolfach, January 1982.
65. Ju. L. Ershov. A question of Jarden and Shelah, Algebra and Logic 28 (1990), 419-420.
66. Ju. L. Ershov. Multi-Valued Fields, Kluwer, 2001.
67. Ju. L. Ershov and M. Fried. Frattini covers and projective groups without the extension property, Mathematische Annalen 253 (1980), 233-239.
68. Ju. L. Ershov, I. A. Lavrov, A.D. Taimanov, and M. A. Taitslin. Elementary theories, Russian Mathematical Surveys 20 (1965), 35-105.
69. G. Faltings, G. Wüstholz, et al. Rational Points, Seminar Bonn/Wuppertal 1983/84, Vieweg, Braunschweig 1984.
70. W. Franz. Untersuchungen zum Hilbertschen Irreduzibilitätssatz, Mathematische Zeit-schrift 33 (1931), 275-193.
71. G. Frey. Pseudo algebraically closed Gelds with non-archimedian real valuations, Journal of Algebra 26 (1973), 202-207.
72. G. Frey and M. Jarden. Approximation theory and the rank of abelian varieties over large algebraic fields, Proceedings of the London Mathematical Society (3) 28 (1974), 112-128.
73. M. Fried. On a conjecture of Schur, Michigan Mathematical Journal 17 (1970), 41-55.
74. M. Fried. On the Diophantine equation f(y) -x = 0, Acta Arithmetica 19 (1971), 79-87.
75. M. Fried. A review to Jarden's paper Elementary statements over algebraic Gelds, Mathematical Reviews 46 (1973), #1975.
76. M. Fried. The field of definition of function fields and a problem in the reducibility of polynomials in two variables, Illinois Journal of Mathematics 17 (1973), 128-146.
77. M. Fried. On Hilbert's irreducibility theorem, Journal of Number Theory 6 (1974), 211-231.
78. M. Fried. On a theorem of MacCluer, Acta Arithmetica 25 (1974), 121-126.
79. M. Fried. Fields of definition of function fields and Hurwitz families - Groups as Galois groups, Communications in Algebra 5 (1) (1977), 17-82.
80. M. Fried. Exposition on arithmetic -group theoretic connection via Riemann's existence theorem, Proceeding of the Santa Cruz conference on finite groups 37 (1980), AMS, 571-602.
81. M. Fried. The nonregular analogue of Tchebotarev's theorem, Pacific Journal of Mathematics 112 (1984), 303-311.
82. M. Fried. On the Sprindzuk-Weissauer approach to universal Hilbert subsets, Israel Journal of Mathematics 51 (1985), 347-363.
83. M. Fried. Variables Separated Polynomials and Moduli Spaces, Number Theory in Progress, eds. K. Gyory, H. Iwaniec, J. Urbanowicz, proceedings of the Schinzel Festschrift, Summer 1997 Zakopane, Walter de Gruyter, Berlin-New York (Feb. 1999), 169-228.
84. M. Fried. Toward a general theory of diophantine problems with applications to p-adic fields, unpublished preprint.
85. M. Fried. Introduction to modular towers, Contemporary Mathematics 186 (1995), 111-171.
86. M. D. Fried, R. Guralnick, and J. Saxl. Schur covers and Carlitz's conjecture, Israel Journal of Mathematics 82 (1993), 157-225.
87. M. Fried, D. Haran, and M. Jarden. Galois stratiGcation over Frobenius Gelds, Advances in Mathematics 51 (1984), 1-35.
88. M. Fried and M. Jarden. Stable extensions and Gelds with the global density property, Canadian Journal of Mathematics 28 (1976), 774-787.
89. M. Fried and M. Jarden. Diophantine properties of subfields of Q, American Journal of Mathematics 100 (1978), 653-666.
90. M. Fried and M. Jarden. Field Arithmetic, Ergebnisse der Mathematik 3 11 (First Edition), Springer-Verlag, Heidelberg, 1986.
91. M. Fried and M. Jarden. On Σ-Hilbertian Gelds, Pacific Journal of Mathematics 185 (1998), 307-313.
92. M. Fried and G. Sacerdote. Solving diophantine problems over all residue class fields of a number field and all finite fields, Annals of Mathematics 104 (1976), 203-233.
93. M. D. Fried and H. Völklein. The inverse Galois problem and rational points on moduli spaces, Mathema-tische Annalen 290 (1991), 771-800.
94. M. Fried and M. Jarden. The embedding problem over a Hilbertian PAC-Geld, Annals of Mathematics 135 (1992), 469-481.
95. G. Frobenius. Über Beziehungen zwischen den Primidealen eines algebraischen Korpers und den Substitutionen seiner Gruppe, Sitzbericht preussische Akademie (1896), 689-703.
96. A. Fröhlich and J. C. Shepherdson. Effective procedures in field theory, Philosophical Transactions of the Royal Society of London 248 (1956), 407-432.
97. W. Gaschütz. Zu einem von B. H. Neumann gestellten Problem, Mathematische Nachrichten 14 (1956) 249-252.
98. W.-D. Geyer. Galois groups of intersections of local fields, Israel Journal of Mathematics 30 (1978), 382-396.
99. W.-D. Geyer. Algebraic function fields of one variable over finite fields are stable, Israel Journal of Mathematics 68 (1989), 102-108.
100. W.-D. Geyer and C. Jensen. Prodihedral groups as Galois groups over number fields, Journal of Number Theory 60 (1996), 332-372.
101. W.-D. Geyer and C. Jensen. Embeddability of quadratic extensions in cyclic extensions, Manuscript, Er-langen, 2000.
102. W.-D. Geyer and M. Jarden. Torsion points of elliptic curves over large algebraic extensions of finitely generated Gelds, Israel Journal of Mathematics 31 (1978), 257-297.
103. W.-D. Geyer and C. Jensen. On the normalizer of finitely generated subgroups of absolute Galois groups of uncountable Hilbertian Gelds of characteristic 0, Israel Journal of Mathematics 63 (1988), 323-334.
104. W.-D. Geyer and C. Jensen. On stable Gelds in positive characteristic, Geometria Dedicatae 29 (1989), 335-375.
105. W.-D. Geyer and C. Jensen. Bounded realization ofl-groups over global Gelds, Nagoya Mathematical Journal 150 (1998), 13-62.
106. W.-D. Geyer and C. Jensen. Non PAC Gelds whose Henselian closures are separably closed, Mathematical Research Letters 8 (2001), 509-519.
107. W.-D. Geyer and C. Jensen. Torsion ofAbelian varieties over large algebraic Gelds, Finite Field Theory and its Applications, Dedicata 36 (1990), 67-87.
108. W. Kimmerle, R. Lyons, R. Sandling, and D. N. Teaque. Composition factors from the group ring and Artin's theorem on the orders of simple groups, Proceedings of the London Mathematical Society (3) 60 (1990), 89-122.
109. N. Klingen. Elementar äquivalente Körper und ihre absolute Galoisgruppe, Archiv der Mathematik 25 (1974), 604-612.
110. N. Klingen. Zahlkörper mit gleicher Primzerlegung, Journal für die reine und angewandte Mathematik 299/300 (1978), 342-384.
111. N. Klingen. Atomare Kronecker-Klassen mit speziellen Galoisgruppen, Abhandlungen aus dem mathematischen Seminar Hamburg 48 (1979), 42-53.
112. N. Klingen. Prime Decomposition and Finite Group Theory, Oxford University Press, 1998.
113. U. Kiefe. Sets definable over finite fields: Their zeta-functions, Transactions of AMS 223 (1976), 45-59.
114. I. Kiming. Explicit classifications of some 2-extensions of a field of characteristic different from 2, Canadian Journal of Mathematics 42 (1990), 825-855.
115. R. Klein. Über Hilbertsche Körper, Journal fur die reine und ungewandte Mathematik 337 (1982), 171-194.
116. K. Knopp. Infinite series, The Theory and Application of Infinite Series, Blackie and Son, London, 1928.
117. L. Kronecker. Über die Irreduzibilität von Gleichungen, Werke 2, 85-93; Monatsberichte Deutsche Akademie für Wissenschaft (1880), 155-163.
118. F.-V. Kuhlmann, M. Pank, and P. Roquette. Immediate and purely wild extensions of valued fields, manuscripta mathe-maticae 55 (1986), 39-67.
119. A. G. Kurosh. The theory of groups II, Chelsea, New York, 1960.
120. W. Kuyk. Generic approach to the Galois embedding and extension problem, Journal of Algebra 9 (1968), 393-407.
121. W. Kuyk. Extensions de corps hilbertiens, Journal of Algebra 14 (1970), 112-124.
122. W. Kuyk and H. W. Lenstra Jr. Abelian extensions of arbitrary fields, Mathematische Annalen 216 (1975), 99-104.
123. J. C. Lagarias, H. L. Montogomery and A. M. Odlyzko. A bound for the least prime ideal in the Chebotarev density theorem, Inventions mathematicae 54 (1979), 271-296.
124. S. Lang. On quasi algebraic closure, Annals of Mathematics 55 (1952), 373-390.
125. S. Lang. Abelian varieties, Interscience Publishers, New York, 1959.
126. S. Lang. Diophantine Geometry, Interscience Publishers, New York, 1962.
127. S. Lang. Introduction to Algebraic Geometry, Interscience Publishers, New York, 1964.
128. S. Lang. Algebraic Number Theory, Addison-Wesley, Reading, 1970.
129. S. Lang. Introduction to Algebraic and Abelian Functions, Addison-Wesley, Reading, 1972.
130. S. Lang. Algebra, Third Edition, Addison-Wesley, Reading, 1997.
131. A. Lenstra. Factoring multiinvariant polynomials over finite Gelds, Journal of computation and System Science 30 (1985), 235-248.
132. A. K. Lenstra, H. W. Lenstra Jr., and L. Lovász. Factoring polynomials with rational coefficients, Mathematische Annalen 261 (1982), 515-534.
133. H. W. Lenstra Jr. On the degrees of exceptional polynomials, manuscript.
134. H. Leptin. Ein Darstellungssatz für kompakte total unzusammenhängende Gruppen, Archiv der Mathematik 6 (1995), 371-373.
135. W. J. LeVeque. Topics in number theory I, Addison-Wesley, Reading, 1958.
136. R. Lidl, G. L. Mullen, and G. Turnwald. Dickson Polynomials, Pitman Monographs and Surveys in Pure and Applied Mathematics 65, Longman, Essex, 1993.
137. R. Lidl and H. Niederreiter. Finite fields, Encyclopedia of Mathematics and its applications 20, Addison-Wesley, Reading, 1983.
138. M. W. Liebeck and A. Shalev. Tie probability of generating a finite simple group, London Mathematical Society Lecture Notes 249, 163-173, Cambridge University Press, Cambridge, 1998.
139. C.-K. Lim. Pronilpotent groups, Nanta Mathematica 6 (1973), 58-59.
140. Q. Liu. Tout groupe Gni est un groupe de Galois sur QP (T), Proceedings of the 1993 Seattle AMS Summer Conference, Recent Development in the Inverse Galois Problem.
141. A. Lubotzky. Combinatorial group theory for pro-p-groups, Journal of Pure and Applied Algebra 25 (1982), 311-325.
142. A. Lubotzky. A group theoretic characterization of linear groups, Journal of Algebra 113 (1988), 207-214.
143. A. Lubotzky, Random elements of a free profinite group generate a free subgroup, Illinois Journal of Mathematics 37 (1993), 78-84.
144. A. Lubotzky and L. van dan Dries. Subgroups of free profinite groups and large subfields of Q, Israel Journal of Mathematics 39 (1981), 25-45.
145. A. Lubotzky and D. Segal. Subgroup Growth, Progress in Mathematics 212, Birkhaüser Verlag, Basel, 2003.
146. R. C. Lyndon and P. E. Schupp. Combinatorial Group Theory, Ergebnisse der Mathematik und ihrer Grenzge-biete 89, Springer-Verlag, Berlin, 1997.
147. A. Macintyre. On definable subsets ofp-adic fields, The Journal of Symbolic Logic 41 (1976), 605-610.
148. A. Macintyre, K. McKenna, and L. v. d. Dries. Elimination of quantifiers in algebraic structures, Advances in Mathematics 47 (1983), 74-87.
149. C. R. MacCluer. A reduction of the Chebotarev density theorem to the cyclic case, Acta Arith-metica 15 (1968), 45-47.
150. M. L. Madan and D. J. Madden. On the theory of congruence function fields, Communications in Algebra 8 (1980), 1687-1697.
151. G. Malle and B. H. Matzat. Inverse Galois Theory, Springer, Berlin, 1999.
152. A. Mann. Positively finitely generated groups, Forum Mathematicum 8 (1996), 429-459.
153. H. Matsumura. Commutative ring theory, Cambridge studies in advanced mathematics 8, Cambridge University Press, Cambridge, 1994.
154. B. H. Matzat. Zum Einbettungsproblem der algebraischen Zahlentheorie mit nicht abelschem Kern, Inventiones mathematicae 80 (1985), 365-374.
155. O. V. Melnikov. Normal subgroups of free profinite groups, Mathematics USSR Izvestija 12 (1978), 1-20.
156. O. V. Melnikov. Characterization of accessible subgroups of free profinite groups (Russian), Doklady Akademii Nauk BSSR 22 (1978), 677-680.
157. O. V. Melnikov. Projective limits of free profinite groups (Russian, English summary), Doklady Akademii Nauk BSSR 24, (1980), 968-970, 1051.
158. O. V. Melnikov. Subgroups and the homology of free products of profinite groups. (Russian) Izvestiya Akademii Nauk SSSR, Seriya Matematicheskaya 53 (1989), no. 1, 97-120; translation in Mathematics of the USSR-Izvestiya 34 (1990), no. 1, 97-119.
159. L. Moret-Bailly. Constructions de revetements de courbe pointées, Journal of Algebra 240 (2001), 505-534.
160. P. Miiller. A Weil-bound free proof of Schur's conjecture, Finite fields and their applications 3 (1997), 25-32.
161. D. Mumford. Abelian varieties, Tata Institute of Fundamental Research, Bombay, 1974.
162. D. Mumford. The Red Book of Varieties and Schemes, Lecture Notes in Mathematics 1358, Springer, Berlin, 1988.
163. A. Néron. Modeles minimaux des variétés abeliénnes sur les corps locaux et globaux, IHES Publications Mathematiques 21 (1964).
164. J. Neukirch, A. Schmidt, and K. Wingberg. Cohomology of Number Fields, Grundlehren der mathematischen wissenschaf-ten 323, Springer, 2000, Berlin.
165. K. Neumann. Every Geld is stable, Israel Journal of Mathematics 104 (1998), 221-260.
166. N. Nobusawa. On the embedding problem of fields and Galois algebras, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 26 (1961), 89-92.
167. N. Nikolov and D. Segal. On finitely generated proGnite groups, I: strong completeness and uniform bounds, manuscript, 2003.
168. J. Pas. Igusa local zeta functions and Meuser's invariant functions, Journal of Number Theory 38 (1991), 287-299.
169. F. Pop. Embedding problems over large Gelds, Annals of Mathematics 144 (1996), 1-34.
170. B. Poizat. Une preuve d'un théorème de James Ax sur les extension algébrique de corps, Comptes Rendus de l'Académie des Sciences, Paris 291 (1980), Serie A-245.
171. L. S. Pontryagin. Topological groups, Gordon and Breach, New York, 1966.
172. A. Prestel. Pseudo real closed Gelds, In Set theory and model theory, Lecture Notes in Mathematics 782 (1981), 127-156, Springer-Verlag, Berlin.
173. A. Prestel. Lectures on formally real Gelds, Lecture Notes in Mathematics 1093, Springer-Verlag, Berlin, 1984.
174. A. Prestel and P. Roquette. Formally p-adic Gelds, Lecture Notes in Mathematics 1050, Springer-Verlag, Berlin, 1984.
175. M. O. Rabin. Computable algebra, General theory and theory of computable Gelds, Transactions of AMS 95 (1960), 341-360.
176. M. Raynaud. Revetements de la droite affine en caracteristique p > 0 et conjecture d'Abhyankar, Inventiones Mathematicae 116 (1994), 425-462.
177. H. Reichardt. Der Primdivisorensatz für algebraische Funktionenkörper über einem end-lichen Konstantenkörper, Mathematische Zeitschrift 40 (1936), 713-719.
178. A. Renyi. Probability theory, North-Holland/American Elsevier, Amsterdam, 1970.
179. P. Ribenboim. Theorie des valuations, Les Presses de PUniversité de montréal, Montréal, 1968.
180. L. Ribes. Introduction to proGnite groups and Galois cohomology, Queen's University, Kingston, 1970.
181. L. Ribes. Frattini covers ofproSnite groups, Archiv der Mathematik 44 (1985), 390-396.
182. L. Ribes and P. Zalesskii. ProSnite Groups, Ergebnisse der Mathematik 3 40, Springer, Berlin, 2000.
183. J. F. Ritt. On algebraic functions which can be expressed in terms of radicals, Transactions of AMS 24 (1922), 21-30.
184. A. Robinson. Nonstandard points on algebraic curves, Journal of Number Theory 5 (1973), 301-327.
185. A. Robinson and P. Roquette. On the Gniteness theorem of Siegel and Mahler concerning diophantine equations, Journal of Number Theory 7 (1975), 121-176.
186. P. Roquette. Applications of nonstandard methods to Hilbert irreducibility theorem and related questions, Unpublished notes, Heidelberg, 1975.
187. P. Roquette. Nonstandard aspects of Hilbert's irreducibility theorem, in Model Theory and Algebra, Memorial Tribute to Abraham Robinson, Lecture Notes in Mathematics 498, Springer-Verlag, Berlin, 1975, pp. 231-275.
188. M. Rosenlicht. Equivalence relations on algebraic curves, Annals of Mathematics 56 (1952), 169-191.
189. G. E. Sacks. Saturated Model Theory, Benjamin, Reading, 1972.
190. P. Samuel. Lectures on old and new results on algebraic curves, Tata Institute, Bombay, 1966.
191. A. Schinzel. On a theorem of Bauer and some of its applications, Acta Arithmetica 2 (1968), 333-344.
192. A. Schinzel. Polynomials with Special Regard to Reducibility, Encyclopedia of Mathematics and its Application 77, Cambridge University Press, Cambridge, 2000.
193. F. K. Schmidt. Körper, über denen jede Gleichung durch Radikale auflösbar ist, Sitzungs-berichte der Heidelberg Akademie der Wissenschaften 2 (1933), 37-47.
194. K. Schmidt. Modelltheoretischen Methoden in der algebraischen Geometrie, Diplomarbeit, Kiel, 1970.
195. K. Schmidt. Nonstandard Methods in Field Theory, Ph.D Thesis, Kiel, 1985.
196. W. M. Schmidt. Equations over finite Gelds: An elementary approach, Lecture Notes in Mathematics 536, Springer-Verlag, Berlin, 1976.
197. K. Schmidt. Zur Methode von Stepanov, Acta Arithmetica 24 (1973), 347-367.
198. I. Schur. Über den Zusammenhang zwischen einem Problem der Zahlentheorie ünd einem Satz uber algebraische Funktionen, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-Mathematische Klasse (1923), 123-134.
199. I. Schur. Zur Theorie der einfach transitiven Permutationsgruppen, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-Mathematische Klasse (1933), 598-623.
200. A. Seidenberg. Elements of the Theory of Algebraic Curves, Addison-Wesley, Reading, 1968.
201. J.-P. Serre. Sur la dimension cohomologique des groupes pro Gnis, Topology 3 (1964-1965), 413-420.
202. J.-P. Serre. Zeta and L-functions, in Arithmetical Algebraic Geometry (Schilling, ed.), Harper and Row, New York (1965), 82-92.
203. J.-P. Serre. Abelian l-adic representations and elliptic curves, Benjamin, New York, 1968.
204. J.-P. Serre. Corps locaux, Hermann, Paris, 1968.
205. J.-P. Serre. Proprietés galoisiennes des points d'ordre Gni des courbes elliptiques, Inven-tiones mathematicae 15 (1972), 259-331.
206. J.-P. Serre. Linear representations of finite groups, Springer-Verlag, Berlin, 1977.
207. J.-P. Serre. Quelques applications du Théorème de densité de Chebotarev, Publication Mathématiques, Institut des Hautes Études Scientifiques 54 (1981), 323-401.
208. J.-P. Serre. Sur le nombre des points rationnels d'une courbe algèbrique sur un corps Gni, Comptes Rendus de PAcadémie des Sciences, Paris, sèrie I, 296 (1983), 397-402.
209. J.-P. Serre. Construction de revêtements étales de la droite afGne en charactéristique p, Comptes Rendus de l'Académie des Sciences, Paris, 311 (1990), 341-346.
210. J.-P. Serre. Topics in Galois Theory, Jones and Barlett, Boston 1992.
211. J.-P. Serre. Galois Cohomology, Springer, Berlin, 1997.
212. I. R. Shafarevich. Algebraic number Gelds (Russian), Proceedings of the International Congress of Mathematics 1962, pp. 163-176.
213. S. Shelah. Every two elementarily equivalent models have isomorphic ultrapowers, Israel Journal of Mathematics 10 (1971), 224-233.
214. J. R. Shoenfield. Mathematical Logic, Addison-Wesley, Reading, 1967.
215. W. Specht. Gruppentheorie, Springer-Verlag, Berlin, 1956.
216. V. G. Sprindzuk. Reducibility of polynomials and rational points on algebraic curves, Soviet Mathematics 21 (1980), 331-334.
217. V. G. Sprindzuk. Diophantine equations involving unknown primes, Trudy MIAN SSR 158 (1981), 180-196.
218. R. Stallings. On torsion free groups with inGnitely many ends, Annals of Mathematics 88 (1968), 312-334.
219. S. A. Stepanov. The number of points of a hyperelliptic curve over a finite prime field (Russian), fzvestiya Akademii Nauk SSSR, Ser. Math 33, (1969), 1171-1181; Mathematics of the USSR-Izvestiya 3 (1969), 1103-1114.
220. S. A. Stepanov. An elementary proof of the Hasse-Weil theorem for hyperelliptic curves, Journal of number theory 4 (1972), 118-143.
221. S. A. Stepanov. An elementary method in the theory of equations over finite fields (Russian), Proceeding of the International Congress of Mathematics (Vancouver, B.C. 1974); AMS Translation (2) 109 (1977), 13-20.
222. H. Stichtenoth. Algebraic Function Fields and Codes, Springer-Verlag, Berlin, 1993.
223. K. O. Stöhr and J. F. Voloch. Weierstrass points and curves over finite fields, Proceedings of the London Mathematical Society (3) 52 (1986), 1-19.
224. M. Suzuki. Group Theory I, Grundlehren der mathematischen Wissenschaften 247, Springer-Verlag 1982, New York.
225. T. Tamagawa. On regularly closed Gelds, Contemporary Mathematics 13 (1982), 325-334.
226. A. Tarski. A decision procedure for elementary algebra and geometry, Technical report (prepared by MacCkinsy), The Rand Corporation, Santa Monica, 1948.
227. N. Tschebotarev. Die Bestimmung der Dichtigkeit einer Menge von Primzahlen, welche zu einer gegebenen Substitutionsklasse gehören, Mathematische Annalen 95 (1926), 191-228.
228. E. C. Titchmarsh. The theory of the Riemann Zeta-function, Oxford at the Clarendon Press, 1951.
229. M. A. Tsfasman, S. G. Vlâdut, and T. Zink. Modular curves, Shimura curves, and Goppa codes better than Warshamov-Gilbert bound, Mathematische Nachrichten 109 (1982), 21-28.
230. G. Turnwald. On Schur's conjecture, Journal of Australian Mathematical Scociety (series A) 58 (1995), 312-357.
231. K. Uchida. Separably Hilbertian fields, Kodai Mathematical Journal 3 (1980), 83-95.
232. H. Volklein. Groups as Galois groups -an Introduction, Cambridge Studies in Advanced Mathematics 53, Cambridge University Press, 1996.
233. J. F. Völoch. Ph.D. Thesis, Cambridge, 1984.
234. B. L. v. d. Waerden. Modern Algebra 1, Zweite AuSage, Springer, 1937.
235. B. L. v. d. Waerden. Einführung in die algebraische Geometrie, Springer-Verlag, Berlin, 1973.
236. B. L. v. d. Waerden. Algebra 1, Springer-Verlag, New York, 1991.
237. B. L. v. d. Waerden. Algebra 2, Springer-Verlag, New York, 1991.
238. W. C. Waterhouse. ProSnite groups are Galois groups, Proceedings AMS 42 (1974), 639-640.
239. T. S. Weigel. Residual properties of free groups, Journal of Algebra 160 (1993), 16-41.
240. T. S. Weigel. Residual properties of free groups II, Communications in Algebra 20 (1992), 1395-1425.
241. T. S. Weigel. Residual properties of free groups III, Israel Journal of Mathematics 77 (1992), 65-81.
242. T. S. Weigel. On the proGnite completion of arithmetic groups of split type, in: Lois d'algebres et variétés algébriques (Editor: M. Goze), Collection Travaux en cours 50, 79-101, Hermann, 1996.
243. A. Weil. L'arithmetique sur les courbes algébriques, Thése, Paris 1928 = Acta Mathe-matica 52 (1928), 281-315.
244. A. Weil. Sur les courbes algebriques et les varietes que s'en deduisent, actualites Sci. et Ind. 1041, Hermann, Paris, 1948.
245. A. Weil. The field of definition of a variety, American Journal of Mathematics 78 (1956), 509-524.
246. A. Weil. Adeles and Algebraic Groups, Institute for Advanced Study, Princeton, 1961.
247. A. Weil. Foundations of Algebraic Geometry, American Mathematical Society, Providence, 1962.
248. A. Weil. Basic Number Theory, Springer-Verlag, Berlin, 1967.
249. R. Weissauer. Der Hilbertsche Irreduzibilitätssatz, Journal für die reine und angewandte Mathematik 334 (1982), 203-220.
250. G. Whaples. Algebraic extensions of arbitrary fields, Duke Mathematical Journal 24 (1957), 201-204.
251. W. H. Wheeler. Model-complete theories of pseudo-algebraically closed Gelds, Annals of Mathematical Logic 17 (1979), 205-226.
252. H. Wielandt. Finite Permutation Groups, Academic Press, New York, 1968.
253. f, Journal für die reine und angewandte Mathematik 174 (1936), 237-245.
254. U. Zannier. Note on g-hilbertian Gelds and nonrational curves with the Hilbert property, manuscripta mathematica 97 (1998), 155-162.
255. O. Zariski and P. Samuel. Commutative Algebra I, Springer-Verlag, New York, 1958.
256. O. Zariski and P. Samuel. Commutative Algebra II, Springer-Verlag, New York, 1960.