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摘要翻译：
设k是特征$P>0$的代数闭域，$G_0$是k上的Barsotti-Tate群（或$P$-可除群）。我们用$S$表示$G_0$的特征p上的“代数”局部模，用$G$表示$G_0$在$S$上的泛变形，用$U\子集S$表示$G$的普通轨迹。$g$over$u$的etale部分在$g$的Tate模上产生了$u$的基本群的monodromy表示$\rho$。本文从Igusa的一个著名定理出发，证明了如果$g0$是连通的且是HW-循环的，则$Rho$是满射的。后一个条件等价于Oort的$A$-数的$G_0$等于1，并且$K$上所有连通的一维Barsotti-Tate群都满足这个条件。
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英文标题：
《p-adic Monodromy of the Universal Deformation of a HW-cyclic
Barsotti-Tate Group》
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作者：
Yichao Tian
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Let k be an algebraically closed field of characteristic $p>0$, and $G_0$ be a Barsotti-Tate group (or $p$-divisible group) over k. We denote by $S$ the "algebraic" local moduli in characteristic p of $G_0$, by $G$ the universal deformation of $G_0$ over $S$, and by $U\subset S$ the ordinary locus of $G$. The etale part of $G$ over $U$ gives rise to a monodromy representation $\rho$ of the fundamental group of $U$ on the Tate module of $G$. Motivated by a famous theorem of Igusa, we prove in this article that $\rho$ is surjective if $G_0$ is connected and HW-cyclic. This latter condition is equivalent to that Oort's $a$-number of $G_0$ equals 1, and it is satisfied by all connected one-dimensional Barsotti-Tate groups over $k$.
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PDF链接：
https://arxiv.org/pdf/0708.2022
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