Displaying similar documents to “On p -adic uniformization”

Etale coverings of a Mumford curve

Marius Van Der Put (1983)

Annales de l'institut Fourier

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Let the field K be complete w.r.t. a non-archimedean valuation. Let X / K be a Mumford curve, i.e. the irreducible components of the stable reduction of X have genus 0. The abelian etale coverings of X are constructed using the analytic uniformization Ω → X and the theta-functions on X . For a local field K one rediscovers G . Frey’s description of the maximal abelian unramified extension of the field of rational functions of X .

Geometry of an étale covering of the p -adic upper half plane

Jeremy Teitelbaum (1990)

Annales de l'institut Fourier

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We describe the rigid geometry of the first layer in the tower of coverings of the p -adic upper half plane constructed by Drinfeld. Using our results, we describe the stable fiber at p of certain Shimura curves.