Seminar

Let k be a complete discrete valuation field and f : X -> Y an analytic morphism between k-affinoid spaces (X and Y might be closed polydisc for instance). We prove that the complementary set of the image of f has finitely many connected components with respect to the Berkovich topology.

We will explain this result, which relies essentially on a quantifier elimination theorem for fields with analytic structures due to Leonard Lipshitz.