PreprintCC BY 4.0arXiv
Diagonal cycles on Shtukas and the adjoint L-function
Abstract
We study diagonal cycles on moduli spaces of shtukas for groups of the form H× 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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BibTeX
@misc{wang2026diagonal,
title = {{Diagonal cycles on Shtukas and the adjoint $L$-function}},
author = {Zeyu Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.25237},
eprint = {2607.25237},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.25237},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Diagonal cycles on Shtukas and the adjoint L-function
AU - Zeyu Wang
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2607.25237
UR - https://arxiv.org/abs/2607.25237
AB - We study diagonal cycles on moduli spaces of shtukas for groups of the form H× 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.
ER -