具有自同态结构的p-可除群的积分Hodge多边形
The integral Hodge polygon for $p$-divisible groups with endomorphism structure
AI总结：
本文为带自同态结构的p-可除群引入积分Hodge多边形这一新不变量，揭示其与经典Hodge多边形、Fargues的Harder-Narasimhan多边形及Pappas-Rapoport多边形的关系，并证明其在p进解析族中连续变化。
摘要：
设p为素数，设$\mathcal{O}_F$为$\mathbb{Q}_p$的有限域扩张F的整数环，设$\mathcal{O}_K$为秩1且混合特征为$(0,p)$的完备赋值环。我们引入并研究了“积分Hodge多边形”，这是定义在$\mathcal{O}_K$上并带有$\mathcal{O}_F$作用ι的p-可除群H的一个新不变量。若$F|\mathbb{Q}_p$为非分歧扩张，该不变量还原为经典Hodge多边形，且仅依赖于$(H,ι)$到$\mathcal{O}_K$剩余域的约化。一般情况下并非如此，故冠以“积分”之名。这一新多边形介于Fargues关于H的p幂挠部分的Harder-Narasimhan多边形与另一个称为Pappas-Rapoport多边形的$(H,ι)$组合不变量之间。此外，积分Hodge多边形在p进解析空间上的族中具有连续变化的行为。
英文摘要：
Let $p$ be a prime number, let $\mathcal{O}_F$ be the ring of integers of a finite field extension $F$ of $\mathbb{Q}_p$ and let $\mathcal{O}_K$ be a complete valuation ring of rank $1$ and mixed characteristic $(0,p)$. We introduce and study the "integral Hodge polygon", a new invariant of $p$-divisible groups $H$ over $\mathcal{O}_K$ endowed with an action $ι$ of $\mathcal{O}_F$. If $F|\mathbb{Q}_p$ is unramified, this invariant recovers the classical Hodge polygon and only depends on the reduction of $(H,ι)$ to the residue field of $\mathcal{O}_K$. This is not the case in general, whence the attribute "integral". The new polygon lies between Fargues' Harder-Narasimhan polygons of the $p$-power torsion parts of $H$ and another combinatorial invariant of $(H,ι)$ called the Pappas-Rapoport polygon. Furthermore, the integral Hodge polygon behaves continuously in families over a $p$-adic analytic space.
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