Lectures on Supersingular K3 Surfaces and the Crystalline Torelli Theorem
Algebraic Geometry
2023-02-09 v4 Number Theory
Abstract
We survey crystalline cohomology, crystals, and formal group laws with an emphasis on geometry. We apply these concepts to K3 surfaces, and especially to supersingular K3 surfaces. In particular, we discuss stratifications of the moduli space of polarized K3 surfaces in positive characteristic, Ogus' crystalline Torelli theorem for supersingular K3 surfaces, the Tate conjecture, and the unirationality of K3 surfaces.
Keywords
Cite
@article{arxiv.1403.2538,
title = {Lectures on Supersingular K3 Surfaces and the Crystalline Torelli Theorem},
author = {Christian Liedtke},
journal= {arXiv preprint arXiv:1403.2538},
year = {2023}
}
Comments
63 pages, section on unirationality updated (this version now differs from the published one); K3 Surfaces and Their Moduli, Progress in Mathematics 315, Birkh\"auser (2016), 171-235