Finite polynomial cohomology with coefficients
Ting-Han Huang, Ju-Feng Wu

TL;DR
This paper develops a new finite polynomial cohomology theory with coefficients, establishing foundational properties, an Abel-Jacobi map, and applying it to arithmetic studies of Shimura curves, simplifying existing proofs.
Contribution
It introduces a novel cohomology theory with coefficients, expanding tools for arithmetic geometry and providing streamlined proofs for known results.
Findings
Established basic properties of the cohomology theory
Constructed an Abel-Jacobi map with coefficients
Applied the theory to Shimura curves, simplifying existing proofs
Abstract
We introduce a theory of finite polynomial cohomology with coefficients in this paper. We prove several basic properties and introduce an Abel-Jacobi map with coefficients. As applications, we use such a cohomology theory to study arithmetics of compact Shimura curves over , and simplify proofs of the works of Darmon-Rotger and Bertolini-Darmon-Prasanna.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems · Advanced Combinatorial Mathematics
