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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2412.14313","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2024-12-18T20:26:47Z","cross_cats_sorted":[],"title_canon_sha256":"f7378657128e88144477053efdc71903fa5e56e55507b3876797df320e18e519","abstract_canon_sha256":"cebcce0fc9c936cc7d951f359695fd0f3ec648c63cc551271c0b7327ff5e37a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:34:02.851393Z","signature_b64":"ZKAr8oszOLQJArZzTN9FarmzznUXCLlKjrdwGK8FaJyMVcvaE8ljYJprknVqTy8N36EzizmuCiLjgAVj0J+pCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc86b8cfe9d2438d9501872990d1e1f5cf9922215b6e2bebc56cabe5fcad4ac3","last_reissued_at":"2026-07-05T11:34:02.850938Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:34:02.850938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $q(q^{2}-1)$. 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