Diagonal cycles on Shtukas and the adjoint $L$-function

Zeyu Wang

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arXiv · 2607.25237

Diagonal cycles on Shtukas and the adjoint $L$-function

Zeyu Wang

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Abstract

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.

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Zeyu Wang. 2026-07-28. Diagonal cycles on Shtukas and the adjoint $L$-function. https://arxiv.org/abs/2607.25237

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