A Friedlander-Suslin theorem over a noetherian base ring

Abstract

Let $k$ be a noetherian commutative ring and let $G$ be a finite flat group scheme over $k$. Let $G$ act rationally on a finitely generated commutative $k$-algebra $A$. We show that the cohomology algebra $H^{\ast }(G,A)$ is a finitely generated $k$-algebra. This unifies some earlier results.

final version

References in corpus (2)

• Finite Schur filtration dimension for modules over an algebra with Schur filtration
• Reductivity properties over an affine base