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Sur les espaces analytiques quasi-compacts de dimension 1 sur un corps valué complet ultramétrique. (On quasi-compact 1-dimensional analytic spaces over a complete ultrametric valued field). (French) Zbl 0623.32020

For quasi-compact 1-dimensional rigid analytic spaces X the authors prove structure theorems. Much attention is paid to base fields K that are not algebraically closed. The following questions are solved:
1) When is X an algebraic curve?
2) When can X be embedded into an algebraic curve?
3) What are the open affinoid subsets of X?
4) What analytic reductions does X have?
Reviewer: M.van der Put

MSC:

32P05 Non-Archimedean analysis
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