Picard rank jumps for K3 surfaces with bad reduction
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
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| _version_ | 1866915056320512000 |
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| author | Tayou, Salim |
| author_facet | Tayou, Salim |
| contents | Let $X$ be a K3 surface over a number field. We prove that $X$ has infinitely many specializations where its Picard rank jumps, hence extending our previous work with Shankar--Shankar--Tang to the case where $X$ might have potentially bad reduction. We prove a similar result for generically ordinary non-isotrivial families of K3 surfaces over curves over $\overline{\mathbb{F}}_p$ which extends previous work of Maulik--Shankar--Tang. As a consequence, we give a new proof of the ordinary Hecke orbit conjecture for orthogonal and unitary Shimura varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_09559 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Picard rank jumps for K3 surfaces with bad reduction Tayou, Salim Number Theory Algebraic Geometry Let $X$ be a K3 surface over a number field. We prove that $X$ has infinitely many specializations where its Picard rank jumps, hence extending our previous work with Shankar--Shankar--Tang to the case where $X$ might have potentially bad reduction. We prove a similar result for generically ordinary non-isotrivial families of K3 surfaces over curves over $\overline{\mathbb{F}}_p$ which extends previous work of Maulik--Shankar--Tang. As a consequence, we give a new proof of the ordinary Hecke orbit conjecture for orthogonal and unitary Shimura varieties. |
| title | Picard rank jumps for K3 surfaces with bad reduction |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2203.09559 |