Birational moduli and nonabelian cohomology

A. Buium

Compositio Mathematica (1988)

  • Volume: 68, Issue: 2, page 175-202
  • ISSN: 0010-437X

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Buium, A.. "Birational moduli and nonabelian cohomology." Compositio Mathematica 68.2 (1988): 175-202. <http://eudml.org/doc/89934>.

@article{Buium1988,
author = {Buium, A.},
journal = {Compositio Mathematica},
keywords = {birational viewpoint; nonabelian cohomology; Global moduli spaces},
language = {eng},
number = {2},
pages = {175-202},
publisher = {Kluwer Academic Publishers},
title = {Birational moduli and nonabelian cohomology},
url = {http://eudml.org/doc/89934},
volume = {68},
year = {1988},
}

TY - JOUR
AU - Buium, A.
TI - Birational moduli and nonabelian cohomology
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 68
IS - 2
SP - 175
EP - 202
LA - eng
KW - birational viewpoint; nonabelian cohomology; Global moduli spaces
UR - http://eudml.org/doc/89934
ER -

References

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  1. 1 M. Artin: Algebraic approximations of structures over complete local rings. Publ. Math. IHES36 (1969) 23-58. Zbl0181.48802MR268188
  2. 2 S.S. Abhyankar, T.T. Moh and M. Van der Put: Invariants of analytic rings. Publ. Math. IHES36 (1969) 165-194. Zbl0193.00402MR260728
  3. 3 A. Borel and J.P. Serre: Théorèmes de finitude en cohomologie Galoisienne. Comm. Math. Helv.39 (1964) 111-164. Zbl0143.05901MR181643
  4. 4 F.A. Bogomolov: Analytic sections in conic bundles. Proc. of the Steklov Institute3 (1985) 17-25. Zbl0579.14014MR752929
  5. 5 A. Buium: Differential Function Fields and Moduli of Algebraic Varieties. Lecture Notes in Math. 1226, Springer (1986). Zbl0613.12018MR874111
  6. 6 A. Buium and M. Takeuchi: Rigidity of maps from Hopf algebras to group algebras, to appear in J. Algebra. Zbl0649.16006MR961322
  7. 7 M. Demazure: Schémas en groupes réductifs. Bull. Soc. Math. France93 (1965) 369-413. Zbl0163.27402MR197467
  8. 8 M. Demazure and P. Gabriel: Groupes Algébriques I. Masson & Cie, Paris, North-Holland, Amsterdam (1970). Zbl0203.23401
  9. 9 M. Demazure and A. Grothendieck: Schémas en Groupes I. Lecture Notes in Math. 151, Springer (1970). Zbl0207.51401MR274458
  10. 10 A. Grothendieck: Séminaire de Géometrie Algébrique. IHES (1960-61). 
  11. 11 F. Grünewald and J.O. Halloran: Nilpotent groups and unipotent algebraic groups. J. Pure Appl. Algebra37(3) (1985) 299-315. Zbl0576.20019MR797867
  12. 12 G.P. Hochschild: Basic Theory of Algebraic Groups and Lie Algebras. Springer (1981). Zbl0589.20025MR620024
  13. 13 G. Heyneman and M.E. Sweedler: Affine Hopf algebras I. J. Algebra13-2(1969) 192-242. Zbl0203.31601MR245570
  14. 14 E.R. Kolchin: Differential Algebra and Algebraic Groups. Academic Press, New York (1973). Zbl0264.12102MR568864
  15. 15 E.R. Kolchin and S. Lang: Existence of invariant bases. Proc. of Amer. Math. Soc.11 (1960) 140-148. Zbl0118.04601MR169841
  16. 16 S. Koizumi: The fields of moduli of polarized abelian varieties. Nagoya Math. J.31 (1968) 185-245. Zbl0246.14006
  17. 17 T. Matsusaka: Algebraic deformations of polarized varieties. Nagoya Math. J.31 (1968) 185-245. Zbl0167.49501MR258827
  18. 18 M. Nagata: Local Rings. Interscience Publishers, New York (1962). Zbl0123.03402MR155856
  19. 19 W. Nichols and B. Weisfeiler: Differential formal groups of J.F. Ritt. Amer. J. Math.104 (5) (1982) 943-1005. Zbl0552.14010MR675306
  20. 20 A. Robert: Automorphism groups of transcendental field extensions. J. Algebra16(2) (1970) 252-271. Zbl0205.06305MR276207
  21. 21 F. Sakai: Kodaira dimension of complements of divisors. In: Complex Analysis and Algebraic Geometry. Tokio, Iwanami (1977) pp. 239-257. Zbl0375.14009MR590433
  22. 22 A. Seidenberg: On analytically equivalent ideals. Publ. Math. IHES36 (1969) 69-74. Zbl0181.32402MR260726
  23. 23 J.P. Serre: Cohomologie Galoisienne. Springer Verlag. Zbl0812.12002
  24. 24 G. Shimura: On the field of rationality for abelian varieties. Nagoya Math. J.45 (1972) 167-178. Zbl0243.14012MR306215
  25. 25 M.E. Sweedler: Hopf Algebras. Benjamin, New York (1969). Zbl0194.32901MR252485
  26. 26 A. Weil: The field of definition of a variety. Amer. J. Math.783 (1956) 509-524. Zbl0072.16001MR82726
  27. 27 M. Rosenlicht: Some basic theorems on algebraic groups. Amer. J. Math.78 (1956) 401-463. Zbl0073.37601MR82183

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