Potential Automorphy of K3 Surfaces with Large Picard Rank
Number Theory
2025-12-05 v1
Abstract
The first part of this paper studied -type abelian varieties and the corresponding compatible systems of representations. Techniques in \cite{BCGP} are applied to show that one can prove the potential modularity of these abelian varieties and compatible systems under some conditions that guarantee a sufficient amount of good primes. Then, in the second part, we use the potential modularity theorems to prove that K3 surfaces over totally real field with Picard rank are potentially modular.
Keywords
Cite
@article{arxiv.2512.04732,
title = {Potential Automorphy of K3 Surfaces with Large Picard Rank},
author = {Chao Gu},
journal= {arXiv preprint arXiv:2512.04732},
year = {2025}
}