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Base change of Invariant subrings

Published online by Cambridge University Press:  11 January 2016

Mitsuyasu Hashimoto
Mitsuyasu Hashimoto*
Affiliation:
Graduate School of Mathematics Nagoya University Chikusa-ku, Nagoya 464-8602Japanhasimoto@math.nagoya-u.ac.jp
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Abstract

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Let R be a Dedekind domain, G an affine flat R-group scheme, and B a flat R-algebra on which G acts. Let A → BG be an R-algebra map. Assume that A is Noetherian. We show that if the induced map K ⊗ A → (K ⊗B)K⊗G is an isomorphism for any algebraically closed field K which is an R-algebra, then S ⊗ A → (S ⊗ B)S⊗G is an isomorphism for any R-algebra S.

Keywords

13A50
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 186 , 2007 , pp. 165 - 171
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

References

[1] Akin, K., Buchsbaum, D. A. and Weyman, J., Schur functors and Schur complexes, Adv. Math., 44 (1982), 207–278.Google Scholar
[2] Bruns, W. and Vetter, U., Determinantal Rings, Lecture Notes in Math. 1327, Springer, 1988.Google Scholar
[3] Concini, C. De and Procesi, C., A characteristic free approach to invariant theory, Adv. Math., 21 (1976), 330–354.Google Scholar
[4] Donkin, S., Rational Representations of Algebraic Groups, Lecture Notes in Math. 1140, Springer, 1985.Google Scholar
[5] Hashimoto, M., Auslander-Buchweitz Approximations of Equivariant Modules, Cambridge, 2000.Google Scholar
[6] Hashimoto, M., Another proof of theorems of De Concini and Procesi, to appear in J. Math. Kyoto Univ. Google Scholar
[7] Jantzen, J. C., Representations of Algebraic Groups, 2nd edition, AMS, 2003.Google Scholar
[8] Mathieu, O., Filtrations of G-modules, Ann. Sci. Ecole Norm. Sup. (4), 23 (1990), 625–644.Google Scholar
[9] Wang, J., Sheaf cohomology on G/B and tensor products of Weyl modules, J. Algebra, 77 (1982), 162–185.Google Scholar