Year: 2026
Type: preprint
Abstract: We develop algorithms to construct a basis of de Rham cohomology for modular curves and a matrix representing the Hodge filtration required in the quadratic Chabauty method. We do this without requiring an explicit plane model of the curve and instead compute these objects in terms of modular forms. Our approach works for any modular curve; to demonstrate its efficiency, we implement our method for nonsplit Cartan modular curves.
Source: arXiv (Cornell University)
Authors: Leonhardt, Marius, Rendell, Isabel
Institutions: Boston University, Max Planck Institute for Mathematics
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223387954