Let k be a complete non-archimedean, algebraically closed field of characteristic 0. We study the different function for finite morphisms of Berkovich curves and investigate its roles as a measurement of the change of radii of discs over which the morphisms are isomorphisms. This property is further used to establish the change of intrinsic radius of convergence of p-adic differential equations, provided they are small enough, under a pushforward by a finite etale morphism.
Metric uniformization of morphisms of Berkovich curves via $p$-adic differential equations
Baldassarri Francesco;
2021
Abstract
Let k be a complete non-archimedean, algebraically closed field of characteristic 0. We study the different function for finite morphisms of Berkovich curves and investigate its roles as a measurement of the change of radii of discs over which the morphisms are isomorphisms. This property is further used to establish the change of intrinsic radius of convergence of p-adic differential equations, provided they are small enough, under a pushforward by a finite etale morphism.
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