论文标题
格林功能的代数周期和值
Algebraic Cycles and values of Green's functions
论文作者
论文摘要
我们在动机共同体学组中构建不可塑性的周期$ h^3 _ {\ Mathcal M}（a，{\ Mathbb Q}（2））$，其中$ a $是数字字段或基础功能字段的Abelian表面。当$ a $是模块化曲线上通用椭圆曲线的自我产品时，这些周期可用于证明高级格林功能值的代数结果，类似于概念的概念，kohnen and kohnen and Zagier。我们提出了一种猜想，将我们的工作与最近的Bruinier-Ehlen-Yang的工作有关，该作品在Gross-Kohnen-Zagier的猜想中。
We construct indecomposable cycles in the motivic cohomology group $H^3_{\mathcal M}(A,{\mathbb Q}(2))$ where $A$ is an Abelian surface over a number field or the function field of a base. When $A$ is the self product of the universal elliptic curve over a modular curve, these cycles can be used to prove algebraicity results for values of higher Green's functions, similar to a conjecture of Gross, Kohnen and Zagier. We formulate a conjecture which relates our work with the recent work of Bruinier-Ehlen-Yang on the conjecture of Gross-Kohnen-Zagier.
