# Stefan Schöer: Moret-Bailly families of supersingular abelian varieties

Oberseminar, October 21, 2021.

Generalizing the Moret-Bailly pencil of abelian surfaces to higher dimensions, we construct for each field of characteristic $p > 0$ smooth projective schemes with trivial dualizing sheaf that do not lift to characteristic zero. Our approach heavily relies on local unipotent group schemes, the Beauville–Bogomolov Decomposition for Kähler manifolds with $c_1 = 0$, and equivariant deformation theory in mixed characteristics. This is joint work with Damian Roessler.