At the end of the eighties, Vladimir Berkovich introduced a new way to define p-adic analytic spaces. A surprising feature is that, although p-adic fields are totally discontinuous, the resulting spaces enjoy many nice topological properties: local compactness, local path-connectedness, etc. On the whole, those spaces are very similar to complex analytic spaces. I plan to cover the following topics.

First talk: Berkovich analytification of algebraic varieties, description of the affine line, relation to rigid geometry (Tate's theory)

Tuesday, October 30, 2018 - 10:30am

#### Jerome Poineau

Université de Caen