arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2411.07366math.AG
收藏

具有刚性解析系数的Hodge-Tate分解

A Hodge-Tate decomposition with rigid analytic coefficients

Lucas Gerth

备注：
v2: accepted version, added a subsection on rigid approximation (3.2) and improved the main result (Thm. 1.6), 40 pages, the numbering changed throughout
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文研究了具有局部p-可除系数的Hodge-Tate分解，推广了Faltings和Scholze的结果，并应用于解析Brauer群和几何p-adic Simpson对应关系。

摘要：

设X是一个光滑的紧致刚性解析空间，其定义域是Q_p的完备代数闭包K的扩展。我们为X建立了具有G系数的Hodge-Tate分解，其中G是任何可交换的局部p-可除刚性群。这推广了Faltings和Scholze的Hodge-Tate分解，即G=G_a的情况。为此，我们引入了具有一般局部p-可除系数的Hodge-Tate谱序列的几何类比。我们证明这些谱序列在E_2层退化。我们的结果更一般地适用于光滑族的可交换adic群类，以及光滑紧致映射X→S的相对情形。我们推导出应用于解析Brauer群和几何p-adic Simpson对应关系的应用。

英文摘要：

Let $X$ be a smooth proper rigid analytic space over a complete algebraically closed field extension $K$ of $\mathbb{Q}_p$. We establish a Hodge--Tate decomposition for $X$ with $G$-coefficients, where $G$ is any commutative locally $p$-divisible rigid group. This generalizes the Hodge--Tate decomposition of Faltings and Scholze, which is the case $G=\mathbb{G}_a$. For this, we introduce geometric analogs of the Hodge--Tate spectral sequence with general locally $p$-divisible coefficients. We prove that these spectral sequences degenerate at $E_2$. Our results apply more generally to a class of smooth families of commutative adic groups over $X$ and in the relative setting of smooth proper morphisms $X\rightarrow S$ of smooth rigid spaces. We deduce applications to analytic Brauer groups and the geometric $p$-adic Simpson correspondence.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑