On the geometry of the Drinfeld symmetric space

par Ernst-Ulrich Gekeler (Universität des Saarlandes)

mardi 21 janv. 2020, 10:45 → 11:45 Europe/Paris

Bât. Braconnier, salle Fokko du Cloux (ICJ, Université Lyon 1)

We present some basic facts about the Drinfeld symmetric space Omega = complement of the K-rational hyperplanes in P^(r-1). Here K is a complete local field of arbitrary characteristic with finite residue class field F. Such spaces play a determining role in the theories of Shimura varieties and Drinfeld modular forms, and the representation theory of GL(r,K). Essentially, we sketch the relationship with the associated Bruhat-Tits building and describe the group of units (invertible holomorphic functions) on Omega.