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Christopher Lazda
Fundamental groups and good reduction criteria for curves over positive characteristic local fields
Journal de théorie des nombres de Bordeaux, 29 no. 3 (2017), p. 755-798
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Class. Math.: 11G20, 14F35, 14F30
Keywords: unipotent fundamental groups, function fields, monodromy, $p$-adic cohomology, good reduction

Résumé - Abstract

In this article I define and study the overconvergent rigid fundamental group of a variety over an equicharacteristic local field. This is a non-abelian $(\varphi ,\nabla )$-module over the bounded Robba ring $\mathcal{E}_K^\dagger$, whose underlying unipotent group (after base changing to the Amice ring $\mathcal{E}_K$) is exactly the classical rigid fundamental group. I then use this to prove an equicharacteristic, $p$-adic analogue of Oda’s theorem that a semistable curve over a $p$-adic field has good reduction if and only if the Galois action on its $\ell$-adic unipotent fundamental group is unramified.

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