- exposé - matière potentielle : xxvi
BRUHAT-TITS THEORY FROM BERKOVICH'S POINT OF VIEW. I — REALIZATIONS AND COMPACTIFICATIONS OF BUILDINGS BERTRAND RÉMY, AMAURY THUILLIER AND ANNETTE WERNER March 2009 Abstract: We investigate Bruhat-Tits buildings and their compactifications by means of Berkovich analytic ge- ometry over complete non-Archimedean fields. For every reductive group G over a suitable non-Archimedean field k we define a map from the Bruhat-Tits building B(G,k) to the Berkovich analytic space Gan asscociated with G. Composing this map with the projection of Gan to its flag varieties, we define a family of compactifi- cations of B(G,k). This generalizes results by Berkovich in the case of split groups. Moreover, we show that the boundary strata of the compactified buildings are precisely the Bruhat-Tits buildings associated with a certain class of parabolics. We also investigate the stabilizers of boundary points and prove a mixed Bruhat decomposition theorem for them. Keywords: algebraic group, local field, Berkovich geometry, Bruhat-Tits building, compactification. AMS classification (2000): 20E42, 51E24, 14L15, 14G22.
- spaces associated
- group
- over
- buildings into compact
- berkovich
- archimedean extension
- euclidean building
- bruhat- tits building
- equivariant map
- space very