Displaying similar documents to “Etale coverings of a Mumford curve”

The class group of a one-dimensional affinoid space

Marius Van Der Put (1980)

Annales de l'institut Fourier

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A curve X over a non-archimedean valued field is with respect to its analytic structure a finite union of affinoid spaces. The main result states that the class group of a one dimensional, connected, regular affinoid space Y is trivial if and only if Y is a subspace of P 1 . As a consequence, X has locally a trivial class group if and only if the stable reduction of X has only rational components.

Local-to-global extensions of representations of fundamental groups

Nicholas M. Katz (1986)

Annales de l'institut Fourier

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Let K be a field of characteristic p > 0 , C a proper, smooth, geometrically connected curve over K , and 0 and ∞ two K -rational points on C . We show that any representation of the local Galois group at ∞ extends to a representation of the fundamental group of C - { 0 , ∞ } which is tamely ramified at 0, provided either that K is separately closed or that C is P 1 . In the latter case, we show there exists a unique such extension, called “canonical”, with the property that the image of the geometric fundamental...