Higher Hida theory for Hilbert modular varieties in the totally split case
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866912597169668096 |
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| author | Grossi, Giada |
| author_facet | Grossi, Giada |
| contents | We study $p$-adic properties of the coherent cohomology of some automorphic sheaves on the Hilbert modular variety $X$ for a totally real field $F$ in the case where the prime $p$ is totally split in $F$. More precisely, we develop higher Hida theory à la Pilloni, constructing, for $0\leq q\leq [F:\mathbb{Q}]$, some modules $M^q$ which $p$-adically interpolate the ordinary part of the cohomology groups $H^q(X, \underlineω^κ)$, varying the weight $κ$ of the automorphic sheaf. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_05666 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Higher Hida theory for Hilbert modular varieties in the totally split case Grossi, Giada Number Theory Algebraic Geometry We study $p$-adic properties of the coherent cohomology of some automorphic sheaves on the Hilbert modular variety $X$ for a totally real field $F$ in the case where the prime $p$ is totally split in $F$. More precisely, we develop higher Hida theory à la Pilloni, constructing, for $0\leq q\leq [F:\mathbb{Q}]$, some modules $M^q$ which $p$-adically interpolate the ordinary part of the cohomology groups $H^q(X, \underlineω^κ)$, varying the weight $κ$ of the automorphic sheaf. |
| title | Higher Hida theory for Hilbert modular varieties in the totally split case |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2106.05666 |