Abstract
The goal of this small note is to give a more concise proof of a result due to Berthelot, Esnault, and Rülling in [4]. For a regular, proper, and flat scheme X over a discrete valuation ring of mixed characteristic (0,p), it relates the vanishing of the cohomology of the structure sheaf of the generic fibre of X with the vanishing of the Witt vector cohomology of its special fibre. We use as a critical ingredient results and constructions by Beilinson [2] and Nekovář–Nizioł [14] related to the h-topos over a p-adic field.
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