Thursday 22 Sep 2016Grothendieck-Messing theorems via crystals of relative displays

Oli Gregory - University of Exeter

H103 15:30-16:30

Displays can be thought of as relative versions of Fontaine's strongly divisible lattices, and were introduced by Zink to classify p-divisible groups over rings R in which p is nilpotent. I will show that, under certain conditions, one can associate to a smooth projective R-scheme X a crystal of relative displays on the crystalline site. The crystal of relative displays provides a convenient framework when considering the deformation theory of X; there are applications to Calabi-Yau threefolds and smooth cubic fourfolds.

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