On Irreducible Symplectic Varieties of ${K3}^{[n]}$-type in Positive Characteristic

Abstract

We show that there is a good notion of irreducible sympelectic varieties of ${K3}^{[n]}$-type over an arbitrary field of characteristic zero or $p>n+1$. Then we construct mixed characteristic moduli spaces for these varieties. Our main result is a generalization of Ogus' crystalline Torelli theorem for supersingular K3 surfaces. For applications, we answer a slight variant of a question asked by F. Charles on moduli spaces of sheaves on K3 surfaces and give a crystalline Torelli theorem for supersingular cubic fourfolds.

arXiv comment40 pages. Reference to Langer-Zink's paper is added and some proofs are simplified. Restrictions on $p$ are relaxed. Some inaccuracies corrected

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Cited by in corpus (2)

• Supersingular O'Grady varieties of dimension six
• Galois representations on the cohomology of hyper-Kähler varieties