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Volumn 150, Issue 3, 1999, Pages 1109-1149

The Cassels-Tate pairing on polarized abelian varieties

(2)  Poonen, Bjorn a   Stoll, Michael a  

a NONE

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EID: 0033235957     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/121064     Document Type: Article
Times cited : (157)

References (43)
  • 1
    • 0001779549 scopus 로고
    • Cohomology of groups
    • J. W. S. Cassels and A. Fröhlich, eds., Academic Press, London
    • M. F. ATIYAH and C. T. C. WALL, Cohomology of groups, in Algebraic Number Theory, 94-115 (J. W. S. Cassels and A. Fröhlich, eds.), Academic Press, London, 1967.
    • (1967) Algebraic Number Theory , pp. 94-115
    • Atiyah, M.F.1    Wall, C.T.C.2
  • 2
    • 0033095103 scopus 로고    scopus 로고
    • Rational points of the group of components of a néron model
    • B. BOSCH and Q. LIU, Rational points of the group of components of a Néron model, Mannscripta Math. 98 (1999), 275-293.
    • (1999) Mannscripta Math. , vol.98 , pp. 275-293
    • Bosch, B.1    Liu, Q.2
  • 4
    • 84941504750 scopus 로고
    • Arithmetic on curves of genus 1, IV. Proof of the Hauptvermutung
    • J. W. S. CASSELS, Arithmetic on curves of genus 1, IV. Proof of the Hauptvermutung, J. reine angew. Math. 211 (1962), 95-112.
    • (1962) J. Reine Angew. Math. , vol.211 , pp. 95-112
    • Cassels, J.W.S.1
  • 5
    • 18244422332 scopus 로고    scopus 로고
    • Zéro-cycles sur les variétés p-adiques et groupe de brauer
    • J.-L. COLLIOT-THÉLÈNE and S. SAITO, Zéro-cycles sur les variétés p-adiques et groupe de Brauer, Internat. Math. Res. Notices, no. 4, (1996), 151-160.
    • (1996) Internat. Math. Res. Notices , vol.4 , pp. 151-160
    • Colliot-Thélène, J.-L.1    Saito, S.2
  • 6
    • 0030446474 scopus 로고    scopus 로고
    • On large Picard groups and the Hasse principle for curves and K3 surfaces
    • D. CORAY and C. MANOIL, On large Picard groups and the Hasse principle for curves and K3 surfaces, Acta Arith. 76 (1996), 165-189.
    • (1996) Acta Arith. , vol.76 , pp. 165-189
    • Coray, D.1    Manoil, C.2
  • 8
    • 0001800514 scopus 로고
    • The rationality of the Poincaré series associated to the p-adic points on a variety
    • J. DENEF, The rationality of the Poincaré series associated to the p-adic points on a variety, Invent. Math. 77 (1984), 1-23.
    • (1984) Invent. Math. , vol.77 , pp. 1-23
    • Denef, J.1
  • 9
    • 84967770230 scopus 로고    scopus 로고
    • How many zeros of a random polynomial are real?
    • A. EDELMAN and E. KOSTLAN, How many zeros of a random polynomial are real?, Bull. A.M.S. 32 (1995), 1-37: Erratum: 33 (1996), 325.
    • (1995) Bull. A.M.S. , vol.32 , pp. 1-37
    • Edelman, A.1    Kostlan, E.2
  • 10
    • 84967770230 scopus 로고    scopus 로고
    • A. EDELMAN and E. KOSTLAN, How many zeros of a random polynomial are real?, Bull. A.M.S. 32 (1995), 1-37: Erratum: 33 (1996), 325.
    • (1996) Erratum , vol.33 , pp. 325
  • 11
    • 0009414670 scopus 로고
    • An infinite version of the Chinese remainder theorem
    • T. EKEDAHL, An infinite version of the Chinese remainder theorem, Comment. Math. Univ. St. Paul 40 (1991), 53-59.
    • (1991) Comment. Math. Univ. St. Paul , vol.40 , pp. 53-59
    • Ekedahl, T.1
  • 12
    • 84961485580 scopus 로고
    • A generalisation of the Cassels-Tate pairing
    • M. FLACH, A generalisation of the Cassels-Tate pairing, J. reine. angew. Math. 412 (1990), 113-127.
    • (1990) J. Reine. Angew. Math. , vol.412 , pp. 113-127
    • Flach, M.1
  • 13
    • 0009313861 scopus 로고    scopus 로고
    • Large torsion subgroups of split Jacobians of curves of genus two or three
    • to appear
    • E. HOWE, F. LEPHÉVOST, and B. POONEN, Large torsion subgroups of split Jacobians of curves of genus two or three, Forum Math., to appear.
    • Forum Math.
    • Howe, E.1    Lephévost, F.2    Poonen, B.3
  • 14
    • 0009376747 scopus 로고
    • Divisor classes on Shimura curves rational over local fields
    • B. W. JORDAN and R. A. LIVNÉ, Divisor classes on Shimura curves rational over local fields, J. reine angew. Math. 378 (1987), 46-52.
    • (1987) J. Reine Angew. Math. , vol.378 , pp. 46-52
    • Jordan, B.W.1    Livné, R.A.2
  • 15
    • 0009315203 scopus 로고    scopus 로고
    • On Atkin-Lehner quotients of Shimura curves
    • _, On Atkin-Lehner quotients of Shimura curves, Bull. London Math. Soc. 31 (1999), 681-685.
    • (1999) Bull. London Math. Soc. , vol.31 , pp. 681-685
  • 16
    • 0001703764 scopus 로고
    • p-adic interpolation of real analytic Eisenstein series
    • N. KATZ, p-adic interpolation of real analytic Eisenstein series, Ann. of Math. 104 (1976), 459-571.
    • (1976) Ann. of Math. , vol.104 , pp. 459-571
    • Katz, N.1
  • 17
    • 0001138167 scopus 로고
    • Finiteness of E(Q) and III(E, Q) for a subclass of Weil curves (Russian)
    • V. KOLYVAGIN, Finiteness of E(Q) and III(E, Q) for a subclass of Weil curves (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988), 522-540, 670-671; transl. in Math. USSR-Izv. 32 (1989), 523-541.
    • (1988) Izv. Akad. Nauk SSSR Ser. Mat. , vol.52 , pp. 522-540
    • Kolyvagin, V.1
  • 18
    • 0001747821 scopus 로고
    • V. KOLYVAGIN, Finiteness of E(Q) and III(E, Q) for a subclass of Weil curves (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988), 522-540, 670-671; transl. in Math. USSR-Izv. 32 (1989), 523-541.
    • (1989) Math. USSR-Izv. , vol.32 , pp. 523-541
  • 19
  • 20
    • 0003360933 scopus 로고
    • Number theory III: Diophantine geometry
    • Springer-Verlag, New York
    • _(ed.), Number Theory III: Diophantine Geometry. Encycl. of Math. Sciences 60, Springer-Verlag, New York, 1991.
    • (1991) Encycl. of Math. Sciences , vol.60
  • 21
    • 0001396112 scopus 로고
    • Duality theorems for curves over p-adic fields
    • S. LICHTENBAUM, Duality theorems for curves over p-adic fields, Invent. Math. 7 (1969), 120-136.
    • (1969) Invent. Math. , vol.7 , pp. 120-136
    • Lichtenbaum, S.1
  • 22
    • 0000496135 scopus 로고
    • On the number of real roots of a random algebraic equation
    • J. LITTLEWOOD and A. C. OFFORD, On the number of real roots of a random algebraic equation, J. London Math. Soc. 13 (1938), 288-295.
    • (1938) J. London Math. Soc. , vol.13 , pp. 288-295
    • Littlewood, J.1    Offord, A.C.2
  • 23
    • 84958737079 scopus 로고
    • On the number of real roots of a random algebraic equation (II)
    • _, On the number of real roots of a random algebraic equation (II), Proc. Cambridge Philos. Soc. 35 (1939), 133-148.
    • (1939) Proc. Cambridge Philos. Soc. , vol.35 , pp. 133-148
  • 24
    • 0001211577 scopus 로고
    • On definable subsets of p-adic fields
    • A. MACINTYRE, On definable subsets of p-adic fields, J. of Symbolic Logic 41 (1976), 606-610.
    • (1976) J. of Symbolic Logic , vol.41 , pp. 606-610
    • Macintyre, A.1
  • 25
    • 38249016968 scopus 로고
    • Rationality of p-adic poincaré series: Uniformity in p
    • _, Rationality of p-adic Poincaré series: uniformity in p, Ann. of Pure and Applied Logic 49 (1990), 31-74.
    • (1990) Ann. of Pure and Applied Logic , vol.49 , pp. 31-74
  • 26
    • 0009321023 scopus 로고
    • The Brauer group of a rational surface
    • J. S. MILNE, The Brauer group of a rational surface, Invent. Math. 11 (1970), 304-307.
    • (1970) Invent. Math. , vol.11 , pp. 304-307
    • Milne, J.S.1
  • 27
    • 0038890569 scopus 로고
    • Comparison of the Brauer group with the Tate-Šafarevič group
    • 1982
    • _, Comparison of the Brauer group with the Tate-Šafarevič group, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), 735-743 (1982).
    • (1981) J. Fac. Sci. Univ. Tokyo Sect. Ia Math. , vol.28 , pp. 735-743
  • 28
    • 0002627221 scopus 로고
    • Abelian varieties
    • G. Cornell and J.-H. Silverman, eds., Springer-Verlag, New York
    • J. S. MILNE, Abelian varieties, in Arithmetic Geometry, (G. Cornell and J.-H. Silverman, eds.), 103-150, Springer-Verlag, New York, 1986.
    • (1986) Arithmetic Geometry , pp. 103-150
    • Milne, J.S.1
  • 29
    • 0003493006 scopus 로고
    • Academic Press, Inc., Boston, Mass
    • _, Arithmetic Duality Theorems, Academic Press, Inc., Boston, Mass., 1986.
    • (1986) Arithmetic Duality Theorems
  • 30
    • 0003923699 scopus 로고
    • Lectures on curves on an algebraic surface. With a section by G. M. Bergman
    • Princeton Univ. Press, Princeton, N.J.
    • D. MUMFORD, Lectures on Curves on an Algebraic Surface. With a Section by G. M. Bergman, Ann. of Math. Studies 59, Princeton Univ. Press, Princeton, N.J., 1966.
    • (1966) Ann. of Math. Studies , vol.59
    • Mumford, D.1
  • 32
    • 0003324786 scopus 로고
    • Abelian varieties
    • second edition, Oxford University Press, London
    • _, Abelian Varieties, second edition, Tata Inst. of Fund. Res. Studies in Math., no. 5, Oxford University Press, London, 1975.
    • (1975) Tata Inst. of Fund. Res. Studies in Math. , vol.5
  • 33
    • 0031537168 scopus 로고    scopus 로고
    • Explicit descent for Jacobians of cyclic covers of the projective line
    • B. POONEN and E. SCHAEFER, Explicit descent for Jacobians of cyclic covers of the projective line, J. reine angew. Math. 488 (1997), 141-188.
    • (1997) J. Reine Angew. Math. , vol.488 , pp. 141-188
    • Poonen, B.1    Schaefer, E.2
  • 34
    • 0009383565 scopus 로고
    • Tate-Shafarevich groups of elliptic curves with complex multiplication
    • Algebraic Number Theory, Academic Press, Boston, MA
    • K. RUBIN, Tate-Shafarevich groups of elliptic curves with complex multiplication, in Algebraic Number Theory, 409-419, Adv. Stud. Pure Math. 17, Academic Press, Boston, MA, 1989.
    • (1989) Adv. Stud. Pure Math. , vol.17 , pp. 409-419
    • Rubin, K.1
  • 35
    • 0003263196 scopus 로고
    • Real and étale cohomology
    • Springer-Verlag, New York
    • C. SCHEIDERER, Real and Étale Cohomology, Lecture Notes in Math. 1588, Springer-Verlag, New York, 1994.
    • (1994) Lecture Notes in Math. , vol.1588
    • Scheiderer, C.1
  • 37
    • 0013201976 scopus 로고
    • WC-groups over p-adic fields
    • Exposé
    • J. TATE, WC-groups over p-adic fields. Sém. Bourbaki, 10e année: 1957/1958, Exposé 156.
    • (1957) Sém. Bourbaki, 10e Année , pp. 156
    • Tate, J.1
  • 38
    • 0002992840 scopus 로고
    • Duality theorems in Galois cohomology over number fields
    • Stockholm, Inst. Mittag-LeffLer, Djursholm (1963)
    • _, Duality theorems in Galois cohomology over number fields, in Proc. Internat. Congr. Mathematicians (Stockholm, 1962), 288-295, Inst. Mittag-LeffLer, Djursholm (1963).
    • (1962) Proc. Internat. Congr. Mathematicians , pp. 288-295
  • 39
    • 0038240561 scopus 로고
    • On the conjectures of birch and Swinnerton-Dyer and a geometric analog. Sém. Bourbaki
    • Exp. No. 306; reprinted Dix Exposés sur la Cohomologie des Schémas, North-Holland Publishing Co., Amsterdam, Masson & Cie, Editeur, Paris
    • _, On the conjectures of Birch and Swinnerton-Dyer and a geometric analog. Sém. Bourbaki, Exp. No. 306; reprinted in Dix Exposés sur la Cohomologie des Schémas, 189-214, Adv. Studies in Pure Math. 3, North-Holland Publishing Co., Amsterdam, Masson & Cie, Editeur, Paris, 1968.
    • (1968) Adv. Studies in Pure Math. , vol.3 , pp. 189-214
  • 40
    • 0030502730 scopus 로고    scopus 로고
    • The bilinear form of the Brauer group of a surface
    • T. URABE, The bilinear form of the Brauer group of a surface, Invent. Math. 125 (1996), 557-585.
    • (1996) Invent. Math. , vol.125 , pp. 557-585
    • Urabe, T.1
  • 41
    • 0032105546 scopus 로고    scopus 로고
    • Indices of hyperelliptic curves over p-adic fields
    • J. VAN GEEL and V. YANCHEVSKII, Indices of hyperelliptic curves over p-adic fields, Manuscripta Math. 96 (1998), 317-333.
    • (1998) Manuscripta Math. , vol.96 , pp. 317-333
    • Van Geel, J.1    Yanchevskii, V.2
  • 43
    • 0347322258 scopus 로고
    • Zerlegung reeller algebraischer funktionen in quadrate, schiefkörper über reellem funktionenkörper
    • E. WITT, Zerlegung reeller algebraischer Funktionen in Quadrate, Schiefkörper über reellem Funktionenkörper, J. reine angew. Math. 171 (1934), 4-11.
    • (1934) J. Reine Angew. Math. , vol.171 , pp. 4-11
    • Witt, E.1


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