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

On the supersingular loci of quaternionic Siegel space