English

The trace formula and the existence of PEL type Abelian varieties modulo p

Number Theory 2013-06-11 v2 Algebraic Geometry Representation Theory

Abstract

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.

Keywords

Cite

@article{arxiv.1209.0264,
  title  = {The trace formula and the existence of PEL type Abelian varieties modulo p},
  author = {Arno Kret},
  journal= {arXiv preprint arXiv:1209.0264},
  year   = {2013}
}