Higher Hida and Coleman theories on the modular curve
George Boxer, Vincent Pilloni
TL;DR
This paper develops advanced p-adic Hida and Coleman theories for automorphic line bundles on modular curves, establishing a duality pairing between degree 0 and 1 cohomology groups.
Contribution
It introduces new constructions of Hida and Coleman theories for specific cohomology degrees on modular curves and defines a duality pairing between them.
Findings
Construction of Hida and Coleman theories for degree 0 and 1 cohomology.
Definition of a p-adic duality pairing between the theories.
Framework for further study of automorphic forms in p-adic settings.
Abstract
We construct Hida and Coleman theories for the degree 0 and 1 cohomology of automorphic line bundles on the modular curve and we define a p-adic duality pairing between the theories in degree 0 and 1.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology