On the supersingular loci of quaternionic Siegel space

Oliver Bültel

doi:10.4067/S0719-06462014000300006

On the supersingular loci of quaternionic Siegel space

Authors

Oliver Bültel Mathematische Fakultät, Universität Duisburg-Essen, Thea-Leymann Strasse 9, 45127 Essen, Germany.

DOI:

https://doi.org/10.4067/S0719-06462014000300006

Keywords:

supersingular abelian varieties, Shimura varieties, orthogonal groups

Abstract

The paper studies the supersingular locus of the characteristic p moduli space of principally polarized abelian 8-folds that are equipped with an action of a maximal order in a quaternion algebra, that is non-split at âˆž but split at p. The main result is that its irreducible components are Fermat surfaces of degree p + 1.