
A Mumford curve \(Y\) (over a nonarchimedean field \(k)\) has an admissible covering \({\mathcal U}\) by affinoid subsets of \(\mathbb{P}^1(k)\). Given a morphism \(\varphi : X \to Y\) of degree 2 of nonsingular projective curves over \(k\), the author describes the reduction of \(X\) with respect to \(\varphi^{-1} ({\mathcal U})\); he also lists all possibilities if \(Y\) has genus 2 and \(\varphi\) is unramified. The reviewer found no less then 28 misprints on these 7 pages!
14H30, 14G20, Local ground fields in algebraic geometry, Coverings of curves, fundamental group, 14H25, Mumford curve, reduction of nonsingular curve, double covering
14H30, 14G20, Local ground fields in algebraic geometry, Coverings of curves, fundamental group, 14H25, Mumford curve, reduction of nonsingular curve, double covering
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