On the zeta function of quaternionic Shimura varieties

On the Cohomology of Some Simple Shimura Varieties With Bad Reduction

“…In this paper, we concentrate on another special class of Shimura varieties which are related to GL 2 (more precisely, the inner and outer forms of GL 2 ). These varieties were already studied previously by Reimann in [19][20][21][22] and by Kottwitz [12] (the case n = 2 there). Let D be a quaternion division algebra over a totally real number field F, and D × be the associated multiplicative group over Q.…”

“…In this section we will mainly (but not all) follow the notations of [19] section 1. We will also introduce some related unitary Shimura varieties which are special cases of those studied in [12] but not included in the works [19,20,21,22].…”

“…In this paper we assume p is unramified in the totally real field F as in the works [19][20][21][22]. This assumption will imply that the integral models of our Shimura varieties are flat.…”