On the Bloch–Kato conjecture for Hilbert modular forms

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 re...

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Veröffentlicht in:Mathematische Zeitschrift 2021-10, Vol.299 (1-2), p.427-458
1. Verfasser: Tamiozzo, Matteo
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-020-02689-0