Higher Hida theory for Drinfeld modular curves

2025/07/10 by Daniel Barrera Salazar, Salazar, Daniel Barrera, Héctor del Castillo +3
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2507.07423

Abstract

Inspired by the construction of Higher Hida theory of Boxer and Pilloni, we develop Higher Hida theory for the cohomology of the line bundles of Drinfeld modular forms on the Drinfeld modular curve. We also interpolate Serre duality.

Citations

• Modularity theorems for abelian surfaces
• Arithmetic Satake compactifications and algebraic Drinfeld modular forms
• Higher Hida and Coleman theories on the modular curve
• The generic monodromy of Drinfeld modular varieties in special\n characteristic
• Duality of Drinfeld modules and \wp-adic properties of Drinfeld modular forms
• Compactification of Drinfeld modular varieties and Drinfeld Modular Forms of Arbitrary Rank

Related

• Higher Hida and Coleman theories on the modular curve
• Drinfeld modular curve and Weil pairing
• Drinfeld modular curves have many points
• Drinfeld modular forms of arbitrary rank, Part I: Analytic Theory
• A note on Gekeler's h-function