Algebraic covers : field of moduli versus field of definition

Pierre Dèbes; Jean-Claude Douai

Annales scientifiques de l'École Normale Supérieure (1997)

  • Volume: 30, Issue: 3, page 303-338
  • ISSN: 0012-9593

How to cite

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Dèbes, Pierre, and Douai, Jean-Claude. "Algebraic covers : field of moduli versus field of definition." Annales scientifiques de l'École Normale Supérieure 30.3 (1997): 303-338. <http://eudml.org/doc/82433>.

@article{Dèbes1997,
author = {Dèbes, Pierre, Douai, Jean-Claude},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {algebraic covers; varieties over fields; Galois covers; obstruction; characteristic classes},
language = {eng},
number = {3},
pages = {303-338},
publisher = {Elsevier},
title = {Algebraic covers : field of moduli versus field of definition},
url = {http://eudml.org/doc/82433},
volume = {30},
year = {1997},
}

TY - JOUR
AU - Dèbes, Pierre
AU - Douai, Jean-Claude
TI - Algebraic covers : field of moduli versus field of definition
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1997
PB - Elsevier
VL - 30
IS - 3
SP - 303
EP - 338
LA - eng
KW - algebraic covers; varieties over fields; Galois covers; obstruction; characteristic classes
UR - http://eudml.org/doc/82433
ER -

References

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  1. [ArTa] E. ARTIN and J. TATE, Class field theory, W. A. Benjamin, 1967. Zbl0176.33504
  2. [Be] G. V. BELYI, On Galois extensions of a maximal cyclotomic field, (Math. USSR Izvestija, Vol. 14, 12 1980, pp. 247-256). Zbl0429.12004
  3. [CoHa] K. COOMBES and D. HARBATER, Hurwitz families and arithmetic Galois groups, (Duke Math. J., 52 1985, pp. 821-839). Zbl0601.14023MR87g:14012
  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). Zbl0835.14010MR96b:14015
  5. [Db1] P. DÈBES, Groupes de Galois sur K(T), (Séminaire de Théorie des Nombres, Bordeaux, 2, 1990, pp. 229-243). Zbl0729.12010MR91m:12004
  6. [Db2] P. DÈBES, Covers of ℙ1 over the p-adics, “Recent developments in the Inverse Galois Problem”, (Contemporary Math., Vol. 186, 1995, pp. 217-238). Zbl0856.12004MR96g:12005
  7. [DbDo1] P. DÈBES and J-C. DOUAI, Local-global principle for algebraic covers, Israel J. Math., to appear, 1997. Zbl0915.12003
  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. Zbl0900.65271
  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). Zbl0478.12006MR56 #12006
  12. [Gi] J. GIRAUD, Cohomologie non abélienne, (Grundlehren Math. Wiss. 179, Springer-Verlag, 1971). Zbl0226.14011MR49 #8992
  13. [Mi] J. S. MILNE, Etale Cohomology, Princeton University Press, 1980. Zbl0433.14012MR81j:14002
  14. [SGA1] A. GROTHENDIECK et al., Revêtements étales et groupe fondamental, (Séminaire de Géométrie algébrique 1960/1961, Lecture Notes in Math., 224, 1971). Zbl0234.14002
  15. [Se] J.-P. SERRE, Cohomologie galoisienne, (LNM 5, Springer-Verlag, 4e Edition 1973). Zbl0259.12011MR53 #8030
  16. [We] A. WEIL, The field of definition of a variety, Oeuvres complètes (Collected papers) II, Springer-Verlag, pp. 291-306. 

Citations in EuDML Documents

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  1. Layla Pharamond dit d'Costa, Comparaison de deux notions de rationalité d'un dessin d'enfant
  2. Geoffroy Derome, Corps de définition et points rationnels
  3. Pierre Dèbes, Galois covers with prescribed fibers : the Beckmann-Black problem
  4. Joseph Oesterlé, Dessins d'enfants
  5. Aristides Kontogeorgis, Field of moduli versus field of definition for cyclic covers of the projective line
  6. Layla Pharamond dit d’Costa, Géométrie réelle des dessins d’enfant
  7. Pierre Dèbes, Jean-Claude Douai, Michel Emsalem, Familles de Hurwitz et cohomologie non abélienne
  8. Stefan Wewers, Reduction and lifting of special metacyclic covers
  9. Stéphane Flon, Ramification dans le corps des modules
  10. Stefan Wewers, Stable reduction of three point covers

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