On the Bloch-Kato conjecture for Hilbert modular forms

Matteo Tamiozzo

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arXiv · 1911.05019

On the Bloch-Kato conjecture for Hilbert modular forms

Matteo Tamiozzo

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Abstract

The aim of this paper is to prove inequalities towards instances of the Bloch-Kato conjecture for Hilbert modular forms of parallel weight two, when the order of vanishing of the $L$-function at the central point is zero or one. We achieve this implementing an inductive Euler system argument which relies on explicit reciprocity laws for cohomology classes constructed using congruences of automorphic forms and special points on several Shimura curves.

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Matteo Tamiozzo. 2019-11-12. On the Bloch-Kato conjecture for Hilbert modular forms. https://arxiv.org/abs/1911.05019

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