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arXiv · 2108.11227

Construction of quasi-canonical liftings of K3 surfaces of finite height in odd characteristic

Kentaro Inoue
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Abstract

We construct a quasi-canonical lifting of a $K3$ surface of finite height over a finite field of characteristic $p\geq3$. Such results are previously obtained by Nygaard-Ogus when $p\geq5$. For this purpose, we use the display-theoretic deformation theory developed by Langer, Zink, and Lau. We study the display structure of the crystalline cohomology of deformations of a $K3$ surface of finite height in terms of the Dieudonn\'e display of the enlarged formal Brauer group.

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Kentaro Inoue. 2021-08-25. Construction of quasi-canonical liftings of K3 surfaces of finite height in odd characteristic. https://arxiv.org/abs/2108.11227

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