Explicit Constructions of Ramanujan Complexes of Type ${\tilde{A}}_d$

Abstract

In this paper we present for every $d\ge 2$ and every local field $F$ of positive characteristic, explicit constructions of Ramanujan complexes which are quotients of the Bruhat-Tits building $\B_d(F)$ associated with ${\mathrm{PGL}}_d(F)$.

minor corrections