On ramification filtrations and $p$-adic differential modules, I: equal characteristic case

Liang Xiao

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arXiv · 0801.4962

On ramification filtrations and $p$-adic differential modules, I: equal characteristic case

Liang Xiao

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Abstract

Let $k$ be a complete discretely valued field of equal characteristic $p > 0$ with possibly imperfect residue field and let $G_k$ be its Galois group. We prove that the conductors computed by the arithmetic ramification filtrations on $G_k$ coincide with the differential Artin conductors and Swan conductors of Galois representations of $G_k$. As a consequence, we give a Hasse-Arf theorem for arithmetic ramification filtrations in this case. As applications, we obtain a Hasse-Arf theorem for finite flat group schemes; we also give a comparison theorem between the differential Artin conductors and Borger's conductors.

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Liang Xiao. 2010-06-30. On ramification filtrations and $p$-adic differential modules, I: equal characteristic case. https://arxiv.org/abs/0801.4962

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