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arXiv · 2206.13065

On generalized Fuchs theorem over $p$-adic polyannuli

Peiduo Wang
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Abstract

In this paper, we study finite projective differential modules on $p$-adic polyannuli satisfying the Robba condition. Christol and Mebkhout proved the decomposition theorem (the $p$-adic Fuchs theorem) of such differential modules on one dimensional $p$-adic annuli under certain non-Liouvilleness assumption and Gachet generalized it to higher dimensional cases. On the other hand, Kedlaya proved a generalization of the $p$-adic Fuchs theorem in one dimensional case. We prove Kedlaya's generalized version of $p$-adic Fuchs theorem in higher dimensional cases.

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Peiduo Wang. 2022-06-27. On generalized Fuchs theorem over $p$-adic polyannuli. https://arxiv.org/abs/2206.13065

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