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Jerome Poineau

Jerome Poineau (Strasbourg) посетил Лабораторию алгебраической геометрии в мае 2013 года.

24 мая 2013 года Jerome Poineau выступил с докладом "Berkovich spaces over Z" на внеочередном семинаре Лаборатории.

Аннотация: Although Berkovich spaces usually appear in a non-archimedean setting, their general denition actually allows arbitrary Banach rings as base rings, e.g. Z endowed with the usual absolute value. Over the latter, Berkovich spaces look like fibrations that contain complex analytic spaces as well as p-adic analytic spaces for every prime number p. It is possible to generalize the Weierstrass division theorem to this context and use it to investigate the local properties of the spaces. We deduce that the structure sheaf of a Berkovich space over Z behaves as expected: it is coherent and its stalks are excellent local rings.

Видеозапись доклада:



В период с 21 по 29 мая 2013 г. Jerome Poineau и Antoine Ducros (Paris 6) прочитали миникурс «Introduction to Berkovich analytic spaces».

Лекции состоялись
21.05 (вт., 17.00, ауд. 317), 22.05 (ср., 17.00, ауд. 311), 23.05 (чт., 15.30, ауд. 311), 27.05 (пн., 17.00, ауд. 1001), 28.05 (вт., 17.00, ауд. 317) и 29.05 (ср., 17.00, ауд. 311)
на факультете математики НИУ ВШЭ (ул. Вавилова, д.7).

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).

The course will be understandable to those who know the definition of the field of p-adic numbers Qp.

 

Видеозаписи курса:

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