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.

中文翻译：

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Berthelot、Esnault 和 Rülling 对消失结果的新证明

这篇小笔记的目的是为 [4] 中的 Berthelot、Esnault 和 Rülling 的结果提供更简洁的证明。对于具有混合特征的离散估值环上的规则、适当和平坦方案X$(0,p)$，它将X的通用纤维的结构层的上同调的消失与其特殊纤维的Witt向量上同调的消失联系起来。我们使用 Beilinson [2] 和 Nekovář–Nizioł [14] 与p进场上的 h-topos 相关的结果和构造作为关键成分。