Infinitesimal deformation of p-adic differential equations on Berkovich curves

2008/02/14 by Pulita, Andrea
#11M99 #11S40 #11S80 #12h05 #12h25 #12h99 #FOS: Mathematics #Number Theory (math.NT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0802.1945

Abstract

We show that if a differential equations \mathscrF over a quasi-smooth Berkovich curve X has a certain compatibility condition with respect to an automorphism σ of X, and if the automorphism is sufficiently close to the identity, then \mathscrF acquires a semi-linear action of σ (i.e. lifting that on X). This generalizes the previous works of Yves André, 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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