Hasse-Arf filtrations in $p$-adic analytic geometry -- Fourth Release

Filtrations de type Hasse-Arf et monodromie p-adique

One proves the Crew-Tsuzuki "p-adic local monodromy conjecture" (for local fields of characteristic p>0).

A geometric interpretation of the Hasse-Arf theorem

We give an a geometric interpretation of the Hasse-Arf theorem for function fields using the recently proved Oort conjecture.

Hasse-Arf定理的一个推广

A generalization of the Hasse-Arf theorem

利用Harbater-Katz-Gabber曲线理论，将Hasse-Arf定理推广到正特征完备局部域扩张情形。

Duality, refined partial Hasse invariants and the canonical filtration

Let $G$ be a $p$-divisible group over the ring of integers of $\mathbb{C}_p$, and assume that it is endowed with an action of the ring of integers of a finite unramified extension $F$ of $\mathbb{Q}_p$. Let us fix the type $μ$ of this action on the sheaf of differentials $ω_G$. V. Hernandez, following a construction of Goldring and Nicole, defined partial Hasse invariants for $G$. The product of these invariants is the $μ$-ordinary Hasse invariant, and it is non-zero if and only if the $p$-divisible group is $μ$-ordinary (i.e. the Newton polygon is minimal given the type of the action). \\ We …

Zip 周期映射的 Ogus 原理：通过“Frobenius 与 Hodge 滤过”研究 Hasse 不变量的消失阶

An Ogus Principle for Zip period maps: The Hasse invariant's vanishing order via `Frobenius and the Hodge filtration'

本文将 Ogus 关于 Calabi–Yau 族 Hasse 不变量消失阶与共轭线位置的结果推广到群论 Zip 周期映射，并导出 Shimura 簇及 K3 模空间上的原理。

关于模 $p$ 的 Hilbert 模簇的 Hasse 不变量

On the Hasse invariant of Hilbert modular varieties mod $p$

本文研究了模 $p$ 的 Hilbert 模簇上 Hasse 不变量的消失阶，证明其等于共轭滤过与 Hodge 滤过相交的最大整数，且与 Ekedahl-Oort 层的余维数相同，类比了正特征下 Calabi-Yau 簇的结论。