Higher Hida theory for Drinfeld modular curves
Daniel Barrera Salazar, H\'ector del Castillo, Giovanni Rosso
TL;DR
This paper extends Higher Hida theory to the cohomology of line bundles of Drinfeld modular forms on Drinfeld modular curves, building on Boxer and Pilloni's work, and also interpolates Serre duality.
Contribution
It introduces a novel Higher Hida theory framework for Drinfeld modular forms and cohomology, expanding the scope of p-adic modular form theories.
Findings
Developed Higher Hida theory for Drinfeld modular curves.
Interpolated Serre duality within this new framework.
Provides tools for p-adic analysis of Drinfeld modular forms.
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Advanced Algebra and Geometry