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) (Q1091524)

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?