English

On the supersingular loci of quaternionic Siegel space

Algebraic Geometry 2012-09-18 v1

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 the infinite place, but split at p. The main result is that its irreducible components are Fermat surfaces of degree p+1.

Keywords

Cite

@article{arxiv.1209.3548,
  title  = {On the supersingular loci of quaternionic Siegel space},
  author = {Oliver Bueltel},
  journal= {arXiv preprint arXiv:1209.3548},
  year   = {2012}
}

Comments

The work is partially based on results proved in the author's 1997 Oxford thesis entitled "On the mod-p reduction of ordinary CM points"