Let be the moduli space over of g-dimensional principally polarized abelian varieties and be the supersingular locus of . Oort’s conjecture asserts that when , every geometric generic member in Sg has automorphism group . In this talk we shall discuss the progress of this problem, and sketch the proof of our result using supersingular EO strata, which confirm Oort’s conjecture when g is even and p is greater than 3. This is joint work with Valentijn Karemaker.
