School of Mathematics Seminars and Lectures
Compactification of Bruhat-Tits buildings and Berkovich geometry, an overview
by Prof. Bertrand Remy (University of Lyon-1, France)
Friday, November 25, 2011
from
to
(Asia/Kolkata)
at Colaba Campus ( AG-77 )
at Colaba Campus ( AG-77 )
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. |