Displaying similar documents to “Étale fundamental groups of non-archimedean analytic spaces”

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 .

Covering maps over solenoids which are not covering homomorphisms

Katsuya Eda, Vlasta Matijević (2013)

Fundamenta Mathematicae

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Let Y be a connected group and let f: X → Y be a covering map with the total space X being connected. We consider the following question: Is it possible to define a topological group structure on X in such a way that f becomes a homomorphism of topological groups. This holds in some particular cases: if Y is a pathwise connected and locally pathwise connected group or if f is a finite-sheeted covering map over a compact connected group Y. However, using shape-theoretic techniques and...

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...