The basic stratum of some simple Shimura varieties

Details The basic stratum of some simple Shimura varieties The basic stratum of some simple Shimura varieties

2011-11-29

arxiv.org/abs/1111.6830v1

Mathematics

Number Theory

Scientific paper

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. 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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