Isogenies between K3 Surfaces over \mathbbF_p

2018/10/19 by Ziquan Yang, Yang, Ziquan
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1810.08546

Abstract

We generalize Mukai and Shafarevich's definitions of isogenies between K3 surfaces over ℂ to an arbitrary perfect field and describe how to construct isogenous K3 surfaces over \mathbbF_p by prescribing linear algebraic data when p is large. The main step is to show that isogenies between Kuga-Satake abelian varieties induce isogenies between K3 surfaces, in the context of integral models of Shimura varieties. As a byproduct, we show that every K3 surface of finite height admits a CM lifting under a mild assumption on p.

Cited by

• CM liftings of K3 surfaces over finite fields and their applications to the Tate conjecture

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