Bruhat-Tits Theory from Berkovich's Point of View.<br>I - Realizations and Compactifications of Buildings

Details Bruhat-Tits Theory from Berkovich's Point of View.<br>I - Realizations and Compactifications of Buildings Bruhat-Tits Theory from Berkovich's Point of View.<br>I - Realizations and Compactifications of Buildings

2009-03-06

arxiv.org/abs/0903.1245v1

Mathematics

Algebraic Geometry

Scientific paper

We investigate Bruhat-Tits buildings and their compactifications by means of Berkovich analytic geometry 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 G^an to its flag varieties, we define a family of compactifications 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.

Affiliated with

Also associated with

No associations

Rating

Bruhat-Tits Theory from Berkovich's Point of View.<br>I - Realizations and Compactifications of Buildings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bruhat-Tits Theory from Berkovich's Point of View.<br>I - Realizations and Compactifications of Buildings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bruhat-Tits Theory from Berkovich's Point of View.<br>I - Realizations and Compactifications of Buildings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-136249