Mathematische Annalen

, Volume 356, Issue 2, pp 487–518 | Cite as

The basic stratum of some simple Shimura varieties

Article

Abstract

Under simplifying hypotheses we prove a relation between the \(\ell \)-adic cohomology of the basic stratum of a Shimura variety of PEL-type modulo a prime of good reduction of the reflex field and the cohomology of the complex Shimura variety. In particular we obtain explicit formulas for the number of points in the basic stratum over finite fields. We obtain our results using the trace formula and truncation of the formula of Kottwitz for the number of points on a Shimura variety over a finite fields.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Université Paris-SudOrsay CedexFrance

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