Principal homogeneous spaces over Hensel rings
HTML articles powered by AMS MathViewer
- by Rosario Strano PDF
- Proc. Amer. Math. Soc. 87 (1983), 208-212 Request permission
Abstract:
We prove that if $(A,\underline {a})$ is a Hensel couple and $G$ is an affine, smooth group scheme over $A$ then $H_{\mathrm {et}}^1 (A, G) = H_{\mathrm {et}}^1 (A/\underline {a}, G/\underline {a} G)$.References
- Michel Demazure and Pierre Gabriel, Groupes algébriques. Tome I: Géométrie algébrique, généralités, groupes commutatifs, Masson & Cie, Éditeurs, Paris; North-Holland Publishing Co., Amsterdam, 1970 (French). Avec un appendice Corps de classes local par Michiel Hazewinkel. MR 0302656
- Silvio Greco, Henselization of a ring with respect to an ideal, Trans. Amer. Math. Soc. 144 (1969), 43–65. MR 251030, DOI 10.1090/S0002-9947-1969-0251030-1
- Silvio Greco and Rosario Strano, Quasicoherent sheaves over affine Hensel schemes, Trans. Amer. Math. Soc. 268 (1981), no. 2, 445–465. MR 632537, DOI 10.1090/S0002-9947-1981-0632537-7 A. Grothendieck, Le groupe de Brauer. III: Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam, 1968.
- Laurent Gruson, Une propriété des couples henséliens, Colloque d’Algèbre Commutative (Rennes, 1972) Publ. Sém. Math. Univ. Rennes, Année 1972, Univ. Rennes, Rennes, 1972, pp. 13 (French). MR 0412187
- James S. Milne, Étale cohomology, Princeton Mathematical Series, No. 33, Princeton University Press, Princeton, N.J., 1980. MR 559531
- Rosario Strano, Azumaya algebras over Hensel rings, Pacific J. Math. 61 (1975), no. 1, 295–303. MR 412166
- Rosario Strano, Cohomology of an affine group scheme over a Hensel ring, J. Algebra 47 (1977), no. 1, 138–153. MR 498575, DOI 10.1016/0021-8693(77)90215-0
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 208-212
- MSC: Primary 14F20; Secondary 13J15, 14L15
- DOI: https://doi.org/10.1090/S0002-9939-1983-0681823-0
- MathSciNet review: 681823