English

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

R2 v1 2026-06-21T19:43:17.856Z