{"paper":{"title":"Rational torsion of generalised Drinfeld modular Jacobians of prime power level","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mar Curc\\'o-Iranzo","submitted_at":"2024-12-18T20:26:47Z","abstract_excerpt":"For a prime $\\mathfrak{p} \\subseteq \\mathbb{F}_{q}[T]$ and a positive integer $r$, we consider the generalised Jacobian $J_{0}(\\mathfrak{n})_{\\mathbf{m}}$ of the Drinfeld modular curve $X_{0}(\\mathfrak{n})$ of level $\\mathfrak{n}=\\mathfrak{p}^r$, with respect to the modulus~$\\mathbf{m}$ consisting of all cusps on the modular curve. We show that the $\\ell$-primary part of the group $J_{0}(\\mathfrak{n})_{\\mathbf{m}}(\\mathbb{F}_{q}(T))_{\\rm{tor}}[\\ell^{\\infty}]$ is trivial for all primes $\\ell$ not dividing $q(q^{2}-1)$. Our results establish a function field analogue to those of Yamazaki--Yang f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.14313","kind":"arxiv","version":2},"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/2412.14313/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"}