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Christopher LazdaFundamental groups and good reduction criteria for curves over positive characteristic local fieldsJournal de théorie des nombres de Bordeaux,
29 no.
3 (
2017), p. 755-798, doi:
10.5802/jtnb.1000
Article
PDF
Class. Math.:
11G20,
14F35,
14F30
Keywords: unipotent fundamental groups, function fields, monodromy, $p$-adic cohomology, good reduction
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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