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arXiv · 0802.1945

Infinitesimal deformation of p-adic differential equations on Berkovich curves

Andrea Pulita
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Abstract

We show that if a differential equations $\mathscr{F}$ over a quasi-smooth Berkovich curve $X$ has a certain compatibility condition with respect to an automorphism $\sigma$ of $X$, and if the automorphism is sufficiently close to the identity, then $\mathscr{F}$ acquires a semi-linear action of $\sigma$ (i.e. lifting that on $X$). This generalizes the previous works of Yves Andr\'e, Lucia Di Vizio, and the author about $p$-adic $q$-difference equations. We also obtain an application to Morita's $p$-adic Gamma function, and to related values of $p$-adic $L$-functions.

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Andrea Pulita. 2008-02-14. Infinitesimal deformation of p-adic differential equations on Berkovich curves. https://arxiv.org/abs/0802.1945

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