论文标题
Hirzebruch-Zagier类和五重田的理性椭圆曲线
Hirzebruch-Zagier classes and rational elliptic curves over quintic fields
论文作者
论文摘要
有条件地，在希尔伯特模块化表面和一些较小的技术假设的典型的构想同时，我们在等级$ 0 $中建立了等效的BSD凸台的新实例，其应用于五五位化领域的理性椭圆曲线的算术。关键成分是扭曲的三级产品$ p $ ad-adic $ l $ - 功能的改进，构建兼容的Hirzebruch-Zagier Cycles集合以及将两者构建的明确互惠法。
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.
