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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2401.13230 |
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| _version_ | 1866929690572226560 |
|---|---|
| author | Kazi, Ananyo |
| author_facet | Kazi, Ananyo |
| contents | Let $L$ be a totally real field, and $p$ be a rational prime that is unramified in $L$. We construct overconvergent families of classes of relative de Rham cohomology of the universal abelian scheme over Hilbert modular varieties associated to $L$. We show that these classes come equipped with Gauss-Manin connection. We prove convergence for $p$-adic iteration of this connection, improving upon a technique due to Andreatta-Iovita. We use this to construct a $p$-adic twisted triple product $L$-function associated to finite slope families of Hilbert modular forms, extending work of Blanco-Chacon-Fornea for Hida families. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted Triple Product $p$-adic $L$-function for Finite Slope Families of Hilbert Modular Forms Kazi, Ananyo Number Theory Algebraic Geometry Let $L$ be a totally real field, and $p$ be a rational prime that is unramified in $L$. We construct overconvergent families of classes of relative de Rham cohomology of the universal abelian scheme over Hilbert modular varieties associated to $L$. We show that these classes come equipped with Gauss-Manin connection. We prove convergence for $p$-adic iteration of this connection, improving upon a technique due to Andreatta-Iovita. We use this to construct a $p$-adic twisted triple product $L$-function associated to finite slope families of Hilbert modular forms, extending work of Blanco-Chacon-Fornea for Hida families. |
| title | Twisted Triple Product $p$-adic $L$-function for Finite Slope Families of Hilbert Modular Forms |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2401.13230 |