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arXiv · 2106.05666

Higher Hida theory for Hilbert modular varieties in the totally split case

Giada Grossi
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Abstract

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 \`{a} 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 $H^q(X, \underline{\omega}^{\kappa})$, varying the weight $\kappa$ of the automorphic sheaf.

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Giada Grossi. 2021-06-10. Higher Hida theory for Hilbert modular varieties in the totally split case. https://arxiv.org/abs/2106.05666

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