The basic stratum of some simple Shimura varieties
Number Theory
2012-05-15 v2 Algebraic Geometry
Representation Theory
Abstract
Under simplifying hypotheses we prove a relation between the l-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.
Keywords
Cite
@article{arxiv.1111.6830,
title = {The basic stratum of some simple Shimura varieties},
author = {Arno Kret},
journal= {arXiv preprint arXiv:1111.6830},
year = {2012}
}
Comments
Corrected and updated version