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arXiv · 1605.08226

Riemann-Hurwitz formula for finite morphisms of $p$-adic curves

Velibor Bojković
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Abstract

Given a finite morphism $\varphi:Y\to X$ of quasi-smooth Berkovich curves over a complete, algebraically closed field $k$ of characteristic $0$, we prove a Riemann-Hurwitz formula relating their Euler-Poincar\'e characteristics (calculated using De Rham cohomology of their overconvergent structure sheaf). The main tools are $p$-adic Runge's theorem together with valuation polygons of analytic functions. Using the results obtained, we provide another point of view on Riemann-Hurwitz formula for finite morphisms of curves over algebraically closed fields of positive characteristic.

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Velibor Bojković. 2016-05-26. Riemann-Hurwitz formula for finite morphisms of $p$-adic curves. https://arxiv.org/abs/1605.08226

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