Lecture Series on Berkovich Spaces by Jerome Poineau, Strasbourg

Dates: November 18. and 19.
November 26. and 28.
December 2. and 3.

Lectures will be 10-12

Room: 119 on Mondays, 414 on other days

First Lecture: Introduction and Survey also for non-specialists

Abstract:

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. They already have found numerous applications in several domains: arithmetic geometry, dynamics, motivic integration, etc.

In this course, we will introduce Berkovich spaces and study their basic properties. The program will cover the following topics: - non- Archimedean fields, absolute values - Tate algebras, affinoid algebras and their properties - affinoid spaces - Berkovich spaces - analytification of algebraic varieties - analytic curves (local structure, homotopy type).