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

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 à la Pilloni, constructing, for $0\le q\le [F:\mathbb{Q}]$, 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.

References in corpus (7)

• Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations
• p-adic Cohomology and classicality of overconvergent Hilbert modular forms
• Higher Hida theory and p-adic L-functions for GSp(4)
• Euler systems for Hilbert modular surfaces
• On the Bloch-Kato conjecture for GSp(4)
• Higher Hida and Coleman theories on the modular curve
• Higher Coleman Theory