Algebraic covers: Field of moduli versus field of definition

Annales Scientifiques de l'Ecole Normale Superieure

Volumn 30, Issue 3, 1997, Pages 303-338

  Dèbes, Pierre ^a   Douai, Jean Claude ^a  

^a UNIV LILLE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031498219     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-9593(97)89922-3     Document Type: Article

References (16)

1. [ArTa] E. ARTIN and J. TATE, Class field theory, W. A. Benjamin, 1967.
2. [Be] G. V. BELYI. On Galois extensions of a maximal cyclotomic field, (Math. USSR Izvestija, Vol. 14, 12 1980, pp. 247-256).
3. [CoHa] K. COOMBES and D. HARBATER, Hurwitz families and arithmetic Galois groups, (Duke Math. J., 52 1985, pp. 821-839).
4. [CouGr] J-M. COUVEIGNES and L. GRANBOULAN, Dessins from a geometric point of view, in The Grothendieck theory of Dessins d'Enfants, (Leila Schneps ed., Camb. U. Press, 1995, pp. 79-113).
5. [Db1] P. DÈBES, Groupes de Galois sur K(T), (Séminaire de Théorie des Nombres, Bordeaux, 2, 1990, pp. 229-243):
6. 1 over the p-adics, "Recent developments in the Inverse Galois Problem", (Contemporary Math., Vol. 186, 1995, pp. 217-238).
7. [DbDo1] P. DÈBES and J-C. DOUAI, Local-global principle far algebraic covers, Israel J. Math., to appear, 1997.
8. [DbDo2] P. DÈBES and J-C. DOUAI, Gerbes and covers, preprint, 1997.
9. [DbEm] P. DÈBES and M. EMSALEM, On field of moduli of curves, preprint, 1996.
10. [Dew] E. DEW, Fields of moduli of arithmetic covers, Thesis, 1991.
11. [Fr] M. FRIED, Fields of definition of function fields and Hurwitz families, Groups as Galois groups. (Comm. in Alg., 1, 1977, pp. 17-82).
12. [Gi] J. GIRAUD, Cohomologie non abélienne, (Grundlehren Math. Wiss. 179, Springer-Verlag, 1971).
13. [Mi] J. S. MILNE, Etale Cohomology, Princeton University Press, 1980.
14. [SGA1] A. GROTHENDIECK et al., Revêtements étales et groupe fondamental, (Séminaire de Géométrie algébrique 1960/61, Lecture Notes in Math., 224, 1971).
15. e Edition 1973).
16. [We] A. WEIL, The field of definition of a variety, Oeuvres complètes (Collected papers) II, Springer-Verlag, pp. 291-306.