{"paper":{"title":"Intersections of Hecke correspondences on the modular varieties of $\\mathcal{D}$-elliptic sheaves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fu-Tsun Wei, \\\"Ozge \\\"Ulkem","submitted_at":"2025-01-27T03:11:54Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15746","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.15746/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}