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arXiv · 2501.15746

Intersections of Hecke correspondences on the modular varieties of $\mathcal{D}$-elliptic sheaves

Özge Ülkem·Fu-Tsun Wei
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Abstract

This paper studies the intersections of Hecke correspondences on the modular varieties of $\mathcal{D}$ -elliptic sheaves in the higher-rank setting, where $\mathcal{D}$ is a "maximal order" in a central division algebra $D$ over a global function field $k$. Assuming that $\dim_k(D) = r^2$, where $r$ is a prime distinct from the characteristic of $k$, we express the intersection numbers of Hecke correspondences as suitable combinations of modified Hurwitz class numbers of "imaginary orders". This result establishes a higher-rank analogue of the classical class number relation.

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Özge Ülkem, Fu-Tsun Wei. 2025-01-27. Intersections of Hecke correspondences on the modular varieties of $\mathcal{D}$-elliptic sheaves. https://arxiv.org/abs/2501.15746

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