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@arXiv_mathNT_bot@mastoxiv.page
2024-02-19 08:24:11

This arxiv.org/abs/2005.02520 has been replaced.
link: scholar.google.com/scholar?q=a

Hirzebruch-Zagier classes and rational elliptic curves over quintic fields
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.