发表机构
Massachusetts Institute of Technology（麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究\(H\times H\)型群希格斯丛模空间上对角循环，通过联系其自交数与行列式线丛插入到伴随\(L\)函数高阶导数，得到函数域上一般格罗斯 - 扎吉尔型恒等式及志村簇算术交的猜想图景。
AI 中文摘要
我们研究了\(H\times H\)型群（其中\(H\)是分裂的几乎单的约化群）的希格斯丛模空间上的对角循环，允许任意修改类型。我们将它们的自交数与行列式线丛的插入联系到伴随\(L\)函数的高阶导数。这给出了任意类型群在函数域上的一般格罗斯 - 扎吉尔型恒等式，并为志村簇上的算术交提供了一个平行的猜想图景。
英文摘要
We study diagonal cycles on moduli spaces of shtukas for groups of the form $H\times H$, where $H$ is a split almost simple reductive group, allowing arbitrary modification types. We relate their self-intersection numbers, with insertions of determinant line bundles, to higher derivatives of adjoint $L$-functions. This gives a general Gross--Zagier-type identity over function fields for groups of arbitrary type, and suggests a parallel conjectural picture for arithmetic intersections on Shimura varieties.
Comments25 pages. v2: Corrected a computational error in some constants in Theorem 1.4 and fixed several minor errors
