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Forms of the rings R[X] and R[X, Y]

Published online by Cambridge University Press:  18 May 2009

M. Bryński
M. Bryński
Affiliation:
University of Warsaw
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Let R be a ring and let S = Spec R. Let us consider the étale fini topology on S [5]. By a form of a given S-scheme T we mean any affine S-scheme W that is locally (in the étale fini topology) isomorphic to T. We shall consider forms of the R-schemes T = Spec R[X] and T = Spec R[X, Y].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 2 , September 1972 , pp. 91 - 97
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

REFERENCES

1.Auslander, M. and Goldman, O., The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97 (1960), 367–409.CrossRefGoogle Scholar
2.Borel, A. and Serre, J. P.. Théorèmes de finitude en cohomologie galoisienne, Comment. Math. Helv. 39 (1964), 111–164.CrossRefGoogle Scholar
3.Bourbaki, N., Algèbre commutative, Ch. 1–2 (Paris, 1961).Google Scholar
4.Chase, S. U., Harrison, D. K. and Rosenberg, A., Galois theory and cohomology of commutative rings, Mem. Amer. Math. Soc. no 52 (1965), 15–33.Google Scholar
5.Demazure, M. and Grothendieck, A., Séminaire de Geometrie Algebrique, Exposé 4 (IHES, Paris, 1963).Google Scholar
6.Gilmer, R. W., R-automorphisms of R[X], Proc. London Math. Soc. (3) 18 (1968), 328–336.CrossRefGoogle Scholar
7.Grothendieck, A., Technique de descente et théorèmes d'existence en geometrie algebrique, Séminaire Bourbaki 1958/1959, Exposé 190.Google Scholar
8.Grothendieck, A., Séminaire de Geometrie Algebrique (IHES, Paris, 1960/1961).Google Scholar
9.Grothendieck, A., Eléments de Geometrie Algebrique (IHES, Paris, 1960/1967).Google Scholar
10.Hertzig, D., Forms of algebraic groups, Proc. Amer. Math. Soc. 12 (1961), 657–660.Google Scholar
11.Kulk, A. Van der, On polynomial rings in two variables, Nieuw Arch. Wisk. (3) 1 (1953), 33–41.Google Scholar
12.Kurosh, A. G., Theory of groups (Moscow, 1967).Google Scholar
13.Šafarevič, I. R., On some infinite-dimensional groups, Rend. Mat. e Appl. 25 (1966), 208–212.Google Scholar
14.Villamayor, O. E., Separable algebras and Galois extensions, Osaka Math. J. 4 (1967), 161–171.Google Scholar