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

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.

preprint2013arXivOpen access
Arno Kret
math.RTmath.AGmath.NT
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Arno Kret

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