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arXiv · 2209.10289

Finite polynomial cohomology with coefficients

Ting-Han Huang·Ju-Feng Wu
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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 $\mathbb{Q}$, and simplify proofs of the works of Darmon-Rotger and Bertolini-Darmon-Prasanna.

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Ting-Han Huang, Ju-Feng Wu. 2022-09-21. Finite polynomial cohomology with coefficients. https://arxiv.org/abs/2209.10289

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