PUB - Publikationen an der Universität Bielefeld

Let G be a connected reductive group over Q(p) and let B(G, Q(p)) be the extended Bruhat-Tits building of G over Q(p). Let L be the completion of the maximal unramified extension of Q(p) and let B(G, L) be the building of G over L. By the theorem of Bruhat and Tits, U(G, Q(p)) may be identified with the fixed point set of the Frobenius automorphism sigma acting on B(G, L). A special ease of our main result states that for any c > 0 there exists C > 0 with the property that any point x epsilon B(G, L) with distance d(x, sigma(x)) < c is at distance < C from B(G, Q(p)). The results in this paper constitute a qualitative generalization of a result of Drinfeld.