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» Conférences d’après mars 2011 : nouveau site

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Summer School of Mathematics "Berkovich Spaces"

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Bruhat-Tits Buildings and Analytic Geometry (Lecture 1)
Bertrand Rémy (Lyon) et Amaury Thuillier (Lyon)

5 juillet 2010

Let G be a reductive algebraic group defined over a non-Archimedean local field k. During the 60’s and 70’s, F. Bruhat and J. Tits have been working on a fine description of groups of rational points like G(k). The achievement of this work is a combinatorial description that can be stated in geometric terms, i.e., using the Euclidean building of G over k. The latter space, which is both a complete metric space and a simplicial complex, can be seen in many ways as a (singular) analogue of the Riemannian symmetric space of a semi-simple real Lie group. During the 80’s, V. Berkovich developed an approach to analytic geometry over non-Archimedean complete fields, thus enriching the classical theory due to Tate-Raynaud. From the beginning he mentionned the possibility to combine his theory with Bruhat-Tits’ one. In these talks, we intend to present a joint work with A. Werner, in which we develop and extend Berkovich’s ideas. We show in particular that they enable one to define and describe natural compactifications of the Bruhat-Tits building of a group G over k as above. These compactifications can also be obtained—again by means of Berkovich geometry—by procedures which very much look like Satake’s initial ideas for symmetric spaces. The necessary material concerning Bruhat-Tits theory will be presented during the first lecture.
Lecture 1: July 5, 11:30
Lecture 2: July 6, 10:30
Lecture 3: July 7, 09:00
Lecture 4: July 8, 10:30

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Bertrand Rémy Bertrand Rémy (Lyon)
Bertrand Rémy est professeur de mathématiques à l’université Lyon I (Claude-Bernard), membre de l’Institut Camille Jordan (UFR de mathématiques, UMR 5208 CNRS/Lyon I).

Amaury Thuillier Amaury Thuillier (Lyon)
Amaury Thuillier est maître de conférences à l’université Lyon I (Claude-Bernard), membre de l’Institut Camille Jordan (UFR de mathématiques, UMR 5208 CNRS/Lyon I).