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

2021/06/10 by Giada Grossi, Grossi, Giada
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2106.05666

openalex publication_date 2021/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≤ q≤ [F: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.

Citations

• p-adic Cohomology and classicality of overconvergent Hilbert modular forms
• Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations
• On the Bloch-Kato conjecture for GSp(4)
• Higher Coleman Theory

Related

• Critical Lambda-adic modular forms and bi-ordinary complexes
• Higher Hida and Coleman theories on the modular curve
• Extensions in the cohomology of Hilbert modular varieties
• On certain cohomology groups attached to mathfrakp^\∞-towers\n of quaternionic Hilbert modular varieties
• Hida theory for Shimura varieties of Hodge type