Thomas Zink - Grothendieck-Messing deformation theory for Hyper-Kähler manifolds

This is joint work with Andreas Langer. Let 𝑅 be an artinian local ring with perfect residue class field 𝑘. We define Hyper-Kähler manifolds 𝑋 and their Beauville-Bogomolov form over 𝑅. We give a lifting criterion in the spirit of Grothendieck and Messing. Over the small Witt ring 𝑊̂ (𝑅) we associate a 2-display to 𝑋. If 𝑋 is ordinary and 𝑆 → 𝑅 is a surjection of artinian local rings we show that lifting 𝑋 to 𝑆 is the same as lifting the 2-display of 𝑋.