Year: 2023
Type: article
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 $$H^*(G,A)$$ H ∗ ( G , A ) is a finitely generated k -algebra. This unifies some earlier results: If G is a constant group scheme, then it is a theorem of Evens (Trans. Amer. Math. Soc. 101 , 224–239, 1961, Theorem 8.1), and if k is a field of finite characteristic, then it is a theorem of Friedlander and Suslin (Invent. Math. 127 , 209–270, 1997). If k is a field of characteristic zero, then there is no higher cohomology, so then it is a theorem of invariant theory.
Source: Transformation Groups
Author: Wilberd van der Kallen
Institution: Utrecht University
Language: Latvian
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4385436302