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.Comment: Corrected and updated versio