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تسجيل مستخدم جديدInfinitesimal deformation of p-adic differential equations on Berkovich curves
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Andrea Pulita
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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 Andre, Lucia Di Vizio, and the author about $p$-adic $q$-difference equations. We also obtain an application to Moritas $p$-adic Gamma function, and to related values of $p$-adic $L$-functions.
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