Base change of invariant subrings

Details Base change of invariant subrings Base change of invariant subrings

2005-11-04

arxiv.org/abs/math/0511100v1

Nagoya Math. J. 186 (2007), 165--171

Mathematics

Commutative Algebra

7 pages

Scientific paper

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

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