Year: 2018
Type: preprint
Abstract: 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 $p$.
Source: arXiv (Cornell University)
Author: Yang, Ziquan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2897022057