### On $p$-adic uniformization

Siegfried Bosch (1981-1982)

Groupe de travail d'analyse ultramétrique

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Siegfried Bosch (1981-1982)

Groupe de travail d'analyse ultramétrique

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Van Steen, G. (1994)

Bulletin of the Belgian Mathematical Society - Simon Stevin

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A. J. De Jong (1995)

Compositio Mathematica

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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 ${\mathbf{P}}^{1}$. As a consequence, $X$ has locally a trivial class group if and only if the stable reduction of $X$ has only rational components.

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 $\infty $ two $K$-rational points on $C$. We show that any representation of the local Galois group at $\infty $ extends to a representation of the fundamental group of $C-\{0,\infty \}$ which is tamely ramified at 0, provided either that $K$ is separately closed or that $C$ is ${\mathbf{P}}^{1}$. In the latter case, we show there exists a unique such extension, called “canonical”, with the property that the image of the geometric fundamental...

David Eisenbud, Noam Elkies, Joe Harris, Robert Speiser (1991)

Compositio Mathematica

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