Isogenies Between K3 Surfaces Over.

We generalize Mukai and Shafarevich's definitions of isogenies between K3 surfaces over |${\mathbb{C}}$| to an arbitrary perfect field and describe how to construct isogenous K3 surfaces over |$\bar{{\mathbb{F}}}_p$| 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 |$p$|⁠. [ABSTRACT FROM AUTHOR]