Let $S$ be the spectrum of a discrete valuation ring (we can assume complete or henselian if necessary). Is it true that the étale cohomology group $H_{et}^2(S,\mathbb{Z})$ is zero?If not in general under which conditions on the residue (resp. fraction) field of the ring defining $S$ is this true?
2026-03-27 20:21:14.1774642874
étale cohomology of valuation rings
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