A Crystalline Torelli Theorem for Supersingular K3 Surfaces

  • Arthur Ogus
Part of the Progress in Mathematics book series (PM, volume 36)


I like to argue that crystalline cohomology will play a role in characteristic p analogous to the role of Ilodge theory in characteristic zero. One aspect of this analogy is that the F-crystal structure on crystalline cohomology should reflect deep geometric properties of varieties. This should be especially true of varieties for which the “p-adic part” of their geometry is the most interesting, as seems, often to be true of supersingular varieties in the sense of Shioda [26]. For example, in [19 §6] I proved that supersingular abelian varieties of dimension at least two are determined up to isomorphism by the F-crystal structure (and trace map) on H cris 1 , just as abelian varieties over ℂ are determined by the Ilodge structure on H DR 1 .


Spectral Sequence Finite Type Ample Line Bundle Algebraic Space Kummer Surface 
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© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Arthur Ogus
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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