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According to a conjecture made by Rasmussen and Tamagawa, if we require these fields to be both a pro-$\\ell$ extension of $F(\\mu_{\\ell^{\\infty}})$ and unramified away from $\\ell$, examples are quite rare. Indeed, it is expected that for a fixed dimension and field of definition, there exists such an abelian variety for only a finite number of primes.\n  We prove a uniform version of the conjecture in the case where the ab"},"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":"1305.5241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-22T19:33:26Z","cross_cats_sorted":[],"title_canon_sha256":"40b83aabb7850432744044ebbec3c1386640a768a05f05c2a4146abf0bb776aa","abstract_canon_sha256":"3e229f2b6a93cd7ca7884b92615cfc32d1d91e28087362b4b331d8fbaa52b3c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:06.424529Z","signature_b64":"PmExRVbgeSBxi+bVGt5gajKviQvwQmsx3rVfslKv4kFC++YbBiV6AXscOSHf3u0zhXAD0jTMExLUQbtTgSnbAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccf20874563d8ecd69bbe5d8bd89c9f3d4b161bcb94d1a02528d8e232ba734e6","last_reissued_at":"2026-05-18T03:25:06.423908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:06.423908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Uniform Version of a Finiteness Conjecture for CM Elliptic Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Abbey Bourdon","submitted_at":"2013-05-22T19:33:26Z","abstract_excerpt":"Let A be an abelian variety defined over a number field F. 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