| Description |
Let G be reductive group over a local field k. During the 60's and the
70's, F. Bruhat and J. Tits have been elaborating a very subtle description
of the structure of the group G(k) in geometric terms, using the Euclidean
building of G. The latter object can be seen, from many viewpoints, as an
analogue of the Riemannian symmetric space attached to a real semisimple Lie
group. During the 80's, V. Berkovich has been developing an approach to
analytic geometry over non-Archimedean fields, enriching the classical
theory due to Tate-Raynaud. He also mentioned a natural connection with
Bruhat-Tits theory from the very beginning. In this talk, I will present
joint work with A. Thuillier and A. Werner in which we extend V. Berkovich's
ideas on Bruhat-Tits theory. We also show that they allow one to define and
study compactifications of the Bruhat-Tits building of G over k. These
compactifications can also be obtained by procedures generalizing Satake's
techniques for symmetric spaces.
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