Potential Automorphy of K3 Surfaces with Large Picard Rank
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909943506927616 |
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| author | Gu, Chao |
| author_facet | Gu, Chao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04732 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Potential Automorphy of K3 Surfaces with Large Picard Rank Gu, Chao Number Theory 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. |
| title | Potential Automorphy of K3 Surfaces with Large Picard Rank |
| topic | Number Theory |
| url | https://arxiv.org/abs/2512.04732 |