K3 surfaces of finite height over finite fields

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Arithmetic of K3 surfaces defined over finite fields is investigated. In particular, we show that any K3 surface of finite height over a finite field k of characteristic p > 3 has a quasi-canonical lifting to characteristic 0, and that for any such lifting, the endormorphism algebra of the transcendental cycles, as a Hodge module, is a CM field. The Tate conjecture for the product of certain two K3 surfaces is also proved. We illustrate by examples how to determine explicitly the formal Brauer group associated to a K3 surface over k. Examples discussed here are all of hypergeometric type.
Cor.3.4 added, typos corrected, to appear in J. Math. Kyoto Univ

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Algebraic Geometry, 14J28; 14G15

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http://salesiana.dossiersoluciones.com/handle/123456789/160060

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0709.1979
 http://arxiv.org/abs/0709.1979

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arXiv