Hirzebruch-Zagier classes and rational elliptic curves over quintic fields

2020/05/05 by Michele Fornea, Fornea, Michele, Zhaorong Jin +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2005.02520

Abstract

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.

Citations

• On ordinary ?-adic representations associated to modular forms
• Modular Elliptic Curves and Fermat's Last Theorem
• On the Bloch-Kato conjecture for GSp(4)

Cited by

• Quaternionic big Heegner points over totally real fields

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