Minimal truncations of supersingular p-divisible groups

The supersingular locus of the Shimura variety for GU(1,s)

In this paper we study the supersingular locus of the reduction modulo p of the Shimura variety for GU(1,s) in the case of an inert prime p. Using Dieudonné theory we define a stratification of the corresponding moduli space of p-divisible groups. We describe the incidence relation of this stratification in terms of the Bruhat-Tits building of a unitary group. In the case of GU(1,2), we show that the supersingular locus is equi-dimensional of dimension 1 and is of complete intersection. We give an explicit description of the irreducible components and their intersection behaviour.

Reconstructing $p$-divisible groups from their truncations of small level

Let $k$ be an algebraically closed field of characteristic $p>0$. Let $D$ be a $p$-divisible group over $k$. Let $n_D$ be the smallest non-negative integer for which the following statement holds: if $C$ is a $p$-divisible group over $k$ of the same codimension and dimension as $D$ and such that $C[p^{n_D}]$ is isomorphic to $D[p^{n_D}]$, then $C$ is isomorphic to $D$. To the Dieudonné module of $D$ we associate a non-negative integer $\ell_D$ which is a computable upper bound of $n_D$. If $D$ is a product $\prod_{i\in I} D_i$ of isoclinic $p$-divisible groups, we show that $n_D=\ell_D$; if th…

某些酉 p-可除群的 Traverso 同源猜想

Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups

本文研究签名 (a,b) 的超奇异酉 p-可除群，完整刻画其最小高度，给出同源截断界，并用酉 Shimura 簇的 BT_m 分层重述结果。

Deforming endomorphisms of supersingular Barsotti-Tate groups

The formal deformation space of a supersingular Barsotti-Tate group over of dimension two equipped with an action of Z_{p^2} is known to be isomorphic to the formal spectrum of a power series ring in two variables. If one chooses an extra Z_{p^2}-linear endomorphism of the p-divisible group then the locus in the formal deformation space formed by those deformations for which the extra endomorphism lifts is a closed formal subscheme of codimension two. We give a complete description of the irreducible components of this formal subscheme, compute the multiplicities of these components, and compu…

极化阿贝尔簇何时由其 $p$-可除群确定？

When is a polarised abelian variety determined by its $\boldsymbol{p}$-divisible group?

该研究聚焦亏格$g$的Siegel模簇及其超奇轨迹，通过转化为类数为一问题，明确了超奇轨迹不可约的条件与极化阿贝尔簇由其极化$p$-可除群唯一确定的情形，求解用到质量公式、自同构群及$g=4$时Ekedahl-Oort层分析。

模2的格罗斯向量与素导体的椭圆曲线

Gross vectors modulo 2 and elliptic curves of prime conductor

该研究证明了模2的格罗斯向量张成F_2^{S_p}，由此证明Kazalicki与Kohen的猜想，还得出素导体、根数为+1的正秩椭圆曲线的模次数被4整除、Watkins猜想对秩2此类曲线成立的结论。