Modularity of $d$-elliptic loci with level structure
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911017495166976 |
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| author | Greer, François Lian, Carl Sweeting, Naomi |
| author_facet | Greer, François Lian, Carl Sweeting, Naomi |
| contents | We consider the generating series of special cycles on $\mathcal{A}_1(N)\times \mathcal{A}_g(N)$, with full level $N$ structure, valued in the cohomology of degree $2g$. The modularity theorem of Kudla-Millson for locally symmetric spaces implies that these series are modular. When $N=1$, the images of these loci in $\mathcal{A}_g$ are the $d$-elliptic Noether-Lefschetz loci, which are conjectured to be modular. In the appendix, it is shown that the resulting modular forms are nonzero for $g=2$ when $N\geq 11$ and $N\neq 12$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00957 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modularity of $d$-elliptic loci with level structure Greer, François Lian, Carl Sweeting, Naomi Algebraic Geometry Number Theory We consider the generating series of special cycles on $\mathcal{A}_1(N)\times \mathcal{A}_g(N)$, with full level $N$ structure, valued in the cohomology of degree $2g$. The modularity theorem of Kudla-Millson for locally symmetric spaces implies that these series are modular. When $N=1$, the images of these loci in $\mathcal{A}_g$ are the $d$-elliptic Noether-Lefschetz loci, which are conjectured to be modular. In the appendix, it is shown that the resulting modular forms are nonzero for $g=2$ when $N\geq 11$ and $N\neq 12$. |
| title | Modularity of $d$-elliptic loci with level structure |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2411.00957 |