%0 Journal Article
%T The trace formula and the existence of PEL type Abelian varieties modulo p
%A Arno Kret
%J Mathematics
%D 2012
%I arXiv
%X We show, using the trace formula, that any Newton stratum of a Shimura variety of PEL-type of types (A) and (C) is non-empty at the primes of good reduction. Furthermore we prove conditionally the non-emptiness for Shimura data associated to odd Spin groups. Our results are conditional on Rapoport-Langlands conjecture and Arthur's conjectures on the discrete spectrum. Both these results have been announced by Arthur and Kisin in significant cases.
%U http://arxiv.org/abs/1209.0264v2