论文标题
在Picard of PerfectOdoid封面上
On Picard Groups of Perfectoid Covers of Toric Varieties
论文作者
论文摘要
让$ x $成为一个合适的光滑的感谢您的光滑品种，而Prime残留特性$ p $的完美体面。我们研究了覆盖由Scholze构建的$ x $的PerfectOid Space $ \ Mathcal {X}^{perf} $，表明$ \ text {pic}（\ Mathcal {x}}^{perf} {perf}）$是规范上的异构性，$ \ text {pic}（pic}（x）[x）[p^{p^{p^{ - 1} $。我们还计算了$ \ Mathcal {x}^{perf} $上的线捆绑包的共同体，并建立了扎兹和batyrev-borisov消失的类似物。这概括了第一作者对“ Projectivoid Space”的类似结果。
Let $X$ be a proper smooth toric variety over a perfectoid field of prime residue characteristic $p$. We study the perfectoid space $\mathcal{X}^{perf}$ which covers $X$ constructed by Scholze, showing that $\text{Pic}(\mathcal{X}^{perf})$ is canonically isomorphic to $\text{Pic}(X)[p^{-1}]$. We also compute the cohomology of line bundles on $\mathcal{X}^{perf}$ and establish analogs of Demazure and Batyrev-Borisov vanishing. This generalizes the first author's analogous results for "projectivoid space".
