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We generalize Mukai and Shafarevich's definitions of isogenies between K3surfaces over $\mathbb{C}$ to an arbitrary perfect field and describe how toconstruct isogenous K3 surfaces over $\bar{\mathbb{F}}_p$ by prescribing linearalgebraic data when $p$ is large. The main step is to show that isogeniesbetween Kuga-Satake abelian varieties induce isogenies between K3 surfaces, inthe context of integral models of Shimura varieties. As a byproduct, we showthat every K3 surface of finite height admits a CM lifting under a mildassumption on $p$.

Isogenies between K3 Surfaces over $\bar{\mathbb{F}}_p$