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Bibliographic Details
Main Authors: Fornea, Michele, Jin, Zhaorong
Format: Preprint
Published: 2020
Subjects:
Online Access:https://arxiv.org/abs/2005.02520
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Table of Contents:
  • Conditionally on a conjecture on the étale cohomology of Hilbert modular surfaces and some minor technical assumptions, we establish new instances of the equivariant BSD-conjecture in rank $0$ with applications to the arithmetic of rational elliptic curves over quintic fields. The key ingredients are a refinement of twisted triple product $p$-adic $L$-functions, the construction of a compatible collection of Hirzebruch-Zagier cycles and an explicit reciprocity law relating the two.