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Thursday 02 Oct 2014Grothendieck-Messing deformation theory for Hyperkaehler varieties

Andreas Langer - University of Exeter

Harrison 101 15:00-16:00

For an artinian ring R with perfect residue field we define higher displays
over the small Witt ring. In analogy to p-divisible groups we prove a result
of Grothendieck-Messing type for hyperkaehler varieties:
If X is a Hyperkaehler variety over R ( for example a K3-surface) then
deformations of X over a nilpotent pd-thickening correspond uniquely
to deformations of the associated 2-display resp. its Hodge-filtration.
For the proof we give an algebraic definition of the Beauville-Bogomolov-Form
on the second de Rham cohomology of X and show that for ordinary Hyperkaehler
varieties the associated F-crystal is self-dual under the BB-pairing.
This is joint work with Thomas Zink

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