Let $R$ be a Noetherian domain and let $G$ be a finite group acting on $R[x_1, .., x_n]$ by permuting the $x_i$. Is $H^1(G,R[x_1, .., x_n]) =0$? If not, are there any conditions on $R$ which insure that?
Thanks.
2026-03-29 07:22:16.1774768936
First cohomology and permutation action
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