Abelianization of the second nonabelian Galois cohomology
Mikhail V. Borovoi
Source: Duke Math. J. Volume 72, Number 1
(1993), 217-239.
First Page:
Show
Hide
Primary Subjects:
11E72
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077289218
Mathematical Reviews number (MathSciNet): MR1242885
Zentralblatt MATH identifier: 0849.12011
Digital Object Identifier: doi:10.1215/S0012-7094-93-07209-2
References
[Bo1] M. V. Borovoi, The algebraic fundamental group and abelian Galois cohomology of reductive algebraic groups, preprint, MPI/89–90, Bonn, 1989.
[Bo2] M. V. Borovoi, The Hasse principle for homogeneous spaces, J. Reine Angew. Math. 426 (1992), 179–192.
Mathematical Reviews (MathSciNet): MR93k:14034
Zentralblatt MATH: 0739.14030
Digital Object Identifier: doi:10.1515/crll.1992.426.179
[Br] L. Breen, Théorie de Schreier supérieure, Ann. Sci. École Norm. Sup. (4) 25 (1992), no. 5, 465–514.
Mathematical Reviews (MathSciNet): MR93k:18019
Zentralblatt MATH: 0795.18009
[De] P. Deligne, Variétés de Shimura: interprétation modulaire, et techniques de construction de modèles canoniques, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 247–289.
Mathematical Reviews (MathSciNet): MR81i:10032
Zentralblatt MATH: 0437.14012
[DG] M. Demazure and A. Grothendieck, Schémas en groupes. III: Structure des schémas en groupes réductifs, Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3). Dirigé par M. Demazure et A. Grothendieck. Lecture Notes in Mathematics, Vol. 153, Springer-Verlag, Berlin, 1962/1964.
Mathematical Reviews (MathSciNet): MR43:223c
Zentralblatt MATH: 0212.52810
[DM] P. Deligne and J. S. Milne, Tannakian categories, Lecture Notes in Mathematics, vol. 900, Springer-Verlag, Berlin, 1982, in Hodge Cycles, Motives, and Shimura Varieties.
Mathematical Reviews (MathSciNet): MR84m:14046
Zentralblatt MATH: 0477.14004
[Do1] J.-C. Douai, $2$-cohomologie galoisienne des groupes semi-simples, thèse, Université de Lille I, 1976.
[Do2] J.-C. Douai, $2$-cohomologie galoisienne des groupes semi-simples définis sur les corps locaux, C. R. Acad. Sci. Paris Sér. A-B 280 (1975), no. 6, Aii, A321–A323.
Mathematical Reviews (MathSciNet): MR53:5540
Zentralblatt MATH: 0328.20036
[Do3] J.-C. Douai, Cohomologie galoisienne des groupes semi-simples définis sur les corps globaux, C. R. Acad. Sci. Paris Sér. A-B 281 (1975), no. 24, Ai, A1077–A1080.
Mathematical Reviews (MathSciNet): MR53:637
Zentralblatt MATH: 0362.20030
[Gi] J. Giraud, Cohomologie non-abélienne, Grundlehren Math. Wiss., vol. 179, Springer-Verlag, Berlin, 1971.
Zentralblatt MATH: 0226.14011
Mathematical Reviews (MathSciNet): MR344253
[Ha1]1 G. Harder, Über die Galoiskohomologie halbeinfacher Matrizengruppen. I, Math. Z. 90 (1965), 404–428.
Mathematical Reviews (MathSciNet): MR32:7677
Zentralblatt MATH: 0152.00903
Digital Object Identifier: doi:10.1007/BF01112362
[Ha1]2 G. Harder, Über die Galoiskohomologie halbeinfacher Matrizengruppen. II, Math. Z. 92 (1966), 396–415.
Mathematical Reviews (MathSciNet): MR34:2777
Zentralblatt MATH: 0152.01001
Digital Object Identifier: doi:10.1007/BF01112219
[Ha2] G. Harder, Bericht über neuere Resultate der Galoiskohomologie halbeinfacher Gruppen, Jber. Deutsch. Math.-Verein. 70 (1967/1968), no. Heft 4, Abt. 1, 182–216.
Mathematical Reviews (MathSciNet): MR39:4165
Zentralblatt MATH: 0194.05701
[He] S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1978.
Mathematical Reviews (MathSciNet): MR80k:53081
Zentralblatt MATH: 0451.53038
[Hu] J. E. Humphreys, Linear algebraic groups, Graduate Texts in Mathematics, vol. 21, Springer-Verlag, New York, 1975.
Mathematical Reviews (MathSciNet): MR53:633
Zentralblatt MATH: 0325.20039
[Kn1]1 M. Kneser, Galois-Kohomologie halbeinfacher algebraischer Gruppen über $\germ p$-adischen Körpern. I, Math. Z. 88 (1965), 40–47.
Mathematical Reviews (MathSciNet): MR30:4760
Zentralblatt MATH: 0143.04702
Digital Object Identifier: doi:10.1007/BF01112691
[Kn1]2 M. Kneser, Galois-Kohomologie halbeinfacher algebraischer Gruppen über $\germ p$-adischen Körpern. II, Math. Z. 89 (1965), 250–272.
Mathematical Reviews (MathSciNet): MR32:5658
Zentralblatt MATH: 0143.04702
Digital Object Identifier: doi:10.1007/BF02116869
[Kn2] M. Kneser, Lectures on Galois cohomology of classical groups, Tata Institute of Fundamental Research Lectures on Mathematics, vol. 47, Tata Institute of Fundamental Research, Bombay, 1969.
Mathematical Reviews (MathSciNet): MR49:5195
Zentralblatt MATH: 0246.14008
[Ko] R. E. Kottwitz, Stable trace formula: elliptic singular terms, Math. Ann. 275 (1986), no. 3, 365–399.
Mathematical Reviews (MathSciNet): MR88d:22027
Zentralblatt MATH: 0577.10028
Digital Object Identifier: doi:10.1007/BF01458611
[Mc] S. Mac Lane, Homology, Die Grundlehren der mathematischen Wissenschaften, Bd. 114, Academic Press Inc., Publishers, New York, 1963.
Mathematical Reviews (MathSciNet): MR28:122
Zentralblatt MATH: 0133.26502
[Mi] J. S. Milne, Arithmetic duality theorems, Perspectives in Mathematics, vol. 1, Academic Press Inc., Boston, MA, 1986.
Mathematical Reviews (MathSciNet): MR88e:14028
Zentralblatt MATH: 0613.14019
[Mu] D. Mumford, Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics, No. 5, Published for the Tata Institute of Fundamental Research, Bombay, 1970.
Mathematical Reviews (MathSciNet): MR44:219
Zentralblatt MATH: 0223.14022
[PR] V. P. Platonov and A. S. Rapinchuk, Algebraicheskie gruppy i teoriya chisel, “Nauka”, Moscow, 1991.
Mathematical Reviews (MathSciNet): MR93j:11023
Zentralblatt MATH: 0732.20027
[Ra] A. S. Rapinchuk, The Hasse principle for symmetric spaces, Dokl. Akad. Nauk BSSR 31 (1987), no. 9, 773–776, 859.
Mathematical Reviews (MathSciNet): MR89a:11039
Zentralblatt MATH: 0679.14027
[Sa] J.-J. Sansuc, Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres, J. Reine Angew. Math. 327 (1981), 12–80.
Mathematical Reviews (MathSciNet): MR83d:12010
Zentralblatt MATH: 0468.14007
Digital Object Identifier: doi:10.1515/crll.1981.327.12
[Se1] J.-P. Serre, Cohomologie galoisienne, Lecture Notes in Math., vol. 5, Springer-Verlag, Berlin, 1964.
Zentralblatt MATH: 0128.26303
[Se2] J.-P. Serre, Groupes algébriques et corps de classes, Hermann, Paris, 1975.
Mathematical Reviews (MathSciNet): MR57:6032
Zentralblatt MATH: 0318.14004
[Sp1] T. A. Springer, Nonabelian $H\sp2$ in Galois cohomology, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965), Amer. Math. Soc., Providence, R.I., 1966, pp. 164–182.
Mathematical Reviews (MathSciNet): MR35:195
Zentralblatt MATH: 0193.48902
[Sp2] T. A. Springer, Reductive groups, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 3–27.
Mathematical Reviews (MathSciNet): MR80h:20062
Zentralblatt MATH: 0416.20034
[Sp3] T. A. Springer, Linear algebraic groups, Progress in Mathematics, vol. 9, Birkhäuser Boston, Mass., 1981.
Mathematical Reviews (MathSciNet): MR84i:20002
Zentralblatt MATH: 0453.14022
[St] R. Steinberg, Endomorphisms of linear algebraic groups, Memoirs of the American Mathematical Society, No. 80, American Mathematical Society, Providence, R.I., 1968.
Mathematical Reviews (MathSciNet): MR37:6288
Zentralblatt MATH: 0164.02902
[We] A. Weil, The field of definition of a variety, Amer. J. Math. 78 (1956), 509–524.
Mathematical Reviews (MathSciNet): MR18,601a
Zentralblatt MATH: 0072.16001
Digital Object Identifier: doi:10.2307/2372670
JSTOR: links.jstor.org
Duke Mathematical Journal