Lecture Series on Berkovich Spaces by Jerome Poineau, Strasbourg
Lecture Series on Berkovich Spaces by Jerome Poineau, Strasbourg
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Nov 18, 2013 10:00 AM
to Dec 03, 2013 12:00 AM 
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Dates: November 18. and 19.
November 26. and 28.
December 2. and 3.
Lectures will be 1012
Room: 119 on Mondays, 414 on other days
First Lecture: Introduction and Survey also for nonspecialists
Abstract:
At the end of the eighties, Vladimir Berkovich introduced a new way to define padic analytic spaces. A surprising feature is that, although padic 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).