Potential Automorphy of K3 Surfaces with Large Picard Rank

Chao Gu

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arXiv · 2512.04732

Potential Automorphy of K3 Surfaces with Large Picard Rank

Chao Gu

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Abstract

The first part of this paper studied $\mathrm{GSp}_4$-type abelian varieties and the corresponding compatible systems of $\mathrm{GSp}_4$ 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 $F$ with Picard rank $\ge 17$ are potentially modular.

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Chao Gu. 2025-12-04. Potential Automorphy of K3 Surfaces with Large Picard Rank. https://arxiv.org/abs/2512.04732

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