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p-adic deformation of graph cycles

By Xuanyu Pan

Abstract

In this paper, we show that the infinitesimal Torelli theorem implies the existence of deformations of automorphisms. In the first part, we use Hodge theory and deformation theory to study the deformations of automorphisms of complex projective manifolds. In the second part, we use crystalline cohomology to explore the p-adic analogues of the first part, which generalizes a result of Berthelot and Ogus. The study of the deformations of automorphisms also provides criterions characterizing when the action of the automorphism group of a variety on its cohomology is faithful.Comment: Typos are fixed. Theorem 3.2 and 5.5 in the last version become Theorem 1.4 and 1.7 in the introduction. The abstract and introduction are revised. Any comments are welcome. Submitte

Topics: Mathematics - Algebraic Geometry
Year: 2017
OAI identifier: oai:arXiv.org:1610.03836

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