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Timestamp: 2019-04-19 22:17:05+00:00

Document:
Volume 82, Number 9 (2006), 147-151.
We prove some new results on Corestriction principle for non-abelian cohomology of group schemes over local and global fields or the rings of integers thereof.
Proc. Japan Acad. Ser. A Math. Sci., Volume 82, Number 9 (2006), 147-151.
M. V. Borovoi, The algebraic fundamental group and abelian Galois cohomology of reductive algebraic groups, Max-Planck Inst., MPI/89–90, Bonn, 1990. (Preprint).
M. V. Borovoi, Abelian Galois Cohomology of Reductive Groups, Memoirs of Amer. Math. Soc. 162, 1998.
M. Borovoi, Non-abelian hypercohomology of a group with coefficients in a crossed module, and Galois cohomology. I. A. S. (Preprint).
L. Breen, Bitorseurs et cohomologie non abélienne, in The Grothendieck Festschrift, Vol. I, 401–476, Progr. Math., 86, Birkhäuser, Boston, Boston, MA, 1990.
P. Deligne, Variétés de Shimura: interprétation modulaire, et techniques de construction de modèles canoniques, in Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, 247–289, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979.
J. -C. Douai, 2-Cohomologie galoisienne des groupes semi-simples, Thèse, Université des Sciences et Tech. de Lille 1, 1976.
P. Gille, La $R$-équivalence sur les groupes algébriques réductifs définis sur un corps global, Inst. Hautes Études Sci. Publ. Math. No. 86 (1997), 199–235.
G. Harder, Halbeinfache Gruppenschemata über Dedekindringen, Invent. Math. 4 (1967), 165–191.
K. Kato, S. Saito and, Global class field theory of arithmetic schemes, in Applications of algebraic $K$-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), 255–331, Contemp. Math., 55, Amer. Math. Soc., Providence, RI, 1986.
M. Kneser, Lectures on Galois cohomology of classical groups, Tata Inst. Fund. Res., Bombay, 1969.
Y. A. Nisnevich, Espaces homogènes principaux rationnellement triviaux et arithmétique des schémas en groupes réductifs sur les anneaux de Dedekind, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), no. 1, 5–8.
T. Ono, On the relative theory of Tamagawa numbers, Ann. of Math. (2) 82 (1965), 88–111.
E. Peyre, Galois cohomology in degree three and homogeneous varieties, $K$-Theory 15 (1998), no. 2, 99–145.
M. Demazure et A. Grothendieck, Schémas en groupes. Tom. 1–3, Lectures Notes in Math., vols. 151–153, Springer - Verlag, Berlin, 1970.
M. Artin et A. Grothendieck, Théorie des topos et cohomologie étale des schémas. Tome 3, Lecture Notes in Math., 305, Springer, Berlin, 1973.
N. Q. Th\v ańg, Corestriction principle in nonabelian Galois cohomology, Proc. Japan Acad. Ser. A Math. Sci. 74 (1998), no. 4, 63–67.
N. Q. Th\v ańg, On corestriction principle in non abelian Galois cohomology over local and global fields, J. Math. Kyoto Univ. 42 (2002), no. 2, 287–304.
N. Q. Th\v ańg, Weak corestriction principle for non-abelian Galois cohomology, Homology Homotopy Appl. 5 (2003), no. 1, 219–249. (Electronic).
M. V. Borovoi, The algebraic fundamental group and abelian Galois cohomology of reductive algebraic groups. Preprint Max-Plank Inst., MPI/89–90, Bonn, 1990.
M. V. Borovoi, Abelian Galois Cohomology of Reductive Groups. Memoirs of Amer. Math. Soc. v. 162, 1998.
M. Borovoi, Non-abelian hypercohomology of a group with coefficients in a crossed module, and Galois cohomology. I. A. S. Preprint, 1991–1992.
L. Breen, Bitorseurs et cohomologie non-abélienne; in: Grothendieck Festschrift, v. 1, 401–476, Boston - Birkhäuser, 1990.
P. Deligne, Variétés de Shimura: Interprétation modulaire et techniques de construction de modèles canoniques; in: Proc. Sym. Pure Math. A. M. S. v. 33 (1979), Part 2, 247–289.
J. -C. Douai, 2-Cohomologie galoisienne des groupes semi-simples. Thèse, Université des Sciences et Tech. de Lille 1, 1976.
P. Gille, La R-équivalence sur les groupes réductifs définis sur un corps de nombres. Pub. Math. I. H. E. S., v. 86 (1997), 199–235.
G. Harder, Halbeinfache Gruppenschemata über Dedekindringen. Invent. Math., Bd. 4 (1967), 165–191.
K. Kato and S. Saito, Global class field theory of arithmetic schemes; in: Applications of algebraic $K$-theory to algebraic geometry and number theory, Contemp. Math., 55, Part II, Amer. Math. Soc., Providence, RI, 1986, 255–331.
M. Kneser, Lectures on Galois cohomology of classical groups. Tata Inst. Fund. Res., 1969.
Y. Nisnevich, Espaces homogènes principaux rationellement triviaux et arithmétique des schémas en groupes réductifs sur les anneaux de Dedekind. C. R. Acad. Sci. Paris, Sér. I Math. t. 299 (1984), no. 1, 5–8.
T. Ono, On relative Tamagawa numbers. Ann. Math. 82 (1965), 88–111.
M. Demazure et A. Grothendieck, Schémas en groupes. Tom. 1–3, Lectures Notes in Math., vols. 151–153, Springer - Verlag, 1970.
M. Artin et A. Grothendieck, Théorie des topos et cohomologie étale des schémas. Lecture Notes in Math. v. 305, Springer - Verlag, 1973.
N. Q. Th\v ańg, Corestriction Principle in non-abelian Galois Cohomology. Proceedings of the Japan Academy, v. 74 (1998), 63–67.
N. Q. Th\v ańg, On corestriction Principle in non-abelian Galois cohomology over local and global fields. J. Math. Kyoto Univ. v. 42 (2002), 287–304.
N. Q. Th\v ańg, Weak Corestriction Principle in non-abelian Galois cohomology. Homology. Homotopy and Applications, v. 5 (2003), 219–249. (Electronic).
F. Xu, Corestriction map for spinor norms. (Preprint).

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