TY - JOUR

T1 - Base change of invariant subrings

AU - Hashimoto, Mitsuyasu

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

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U2 - 10.1017/S0027763000009405

DO - 10.1017/S0027763000009405

M3 - Article

AN - SCOPUS:38349126998

VL - 186

SP - 165

EP - 171

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

ER -