On finite group actions on reductive groups and buildings

摘要

Let H be a connected reductive group over a non-archimedean local field k and let F is contained in Aut_k (H) be a finite group of order not divisible by p, the residual characteristic of k. Let G = (H~F)° be the identity component of the subgroup of H consisting of points fixed by F. The main theorem of this paper asserts that the Bruhat-Tits building B(G) of G can be identified with the set of F-fixed points of B(H).