Covers in p-adic analytic geometry and log covers II: cospecialization of the (p′)-tempered fundamental group in higher dimensions
Covers in p-adic analytic geometry and log covers II: cospecialization of the (p′)-tempered fundamental group in higher dimensions
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p-adic 解析几何中的覆盖和对数覆盖 II：更高维度中 (p) 回火基本群的共特化
DOI：
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发表时间：
2009
影响因子：
1.8
通讯作者：
Emmanuel Lepage
中科院分区：
文献类型：
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作者：
Emmanuel Lepage
摘要p-进丛的调和基本群对由有限覆盖拉回后成为Berkovich拓扑的拓扑覆盖的解析覆盖进行了分类。本文构造了具有多稳约简的光滑态射的回火基本群的(p‘)型之间的余专门化同态。我们在另一篇文章中研究了曲线族的问题。为了构造它们，我们首先用赋予其对数结构的约化刻画具有多稳定约化的光滑适当变种的预(p‘)回火基本群，从而定义了对数多稳变种的回火基本群。
Abstract The tempered fundamental group of a p-adic variety classifies analytic étale covers that become topological covers for Berkovich topology after pullback by some finite étale cover. This paper constructs cospecialization homomorphisms between the (p′) versions of the tempered fundamental group of the fibers of a smooth morphism with polystable reduction. We study the question for families of curves in another paper. To construct them, we will start by describing the pro-(p′) tempered fundamental group of a smooth and proper variety with polystable reduction in terms of the reduction endowed with its log structure, thus defining tempered fundamental groups for log polystable varieties.