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Let K_infty be the field generated over K by all the u_n. If K_infty / K is a Galois extension, then it is abelian, and our main result is that it is generated by the torsion points of a relative Lubin-Tate group (a generalization of the usual Lubin-Tate groups). The proof of this"},"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":"1411.7064","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-25T22:58:35Z","cross_cats_sorted":[],"title_canon_sha256":"b648fe63df3f6e1c04e2ad7e9e3e20908d3761d3ee857b25f690ffe02415a0f0","abstract_canon_sha256":"6f8223670c8fcbfaf4cb9b4c4b7f5efb6760100fcd40d5bc33ebcfb2bf9c171c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:15.418355Z","signature_b64":"Drp/sAA5jE/0JA3VcESclcv1JILRKKVZgHyBuOotlk20jGYvRRywZRyt5Joz9YeYgiOkYCqqndApg5JnNhoNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f24b0e88cba13c61b4fbc7a395149425cffab13fc37aa84fb4fd92f8deac6523","last_reissued_at":"2026-05-18T01:30:15.417839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:15.417839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Iterated extensions and relative Lubin-Tate groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Laurent Berger","submitted_at":"2014-11-25T22:58:35Z","abstract_excerpt":"Let K be a finite extension of Q_p with residue field F_q and let P(T) = T^d + a_{d-1}T^{d-1} + ... +a_1 T, where d is a power of q and a_i is in the maximal ideal of K for all i. Let u_0 be a uniformizer of O_K and let {u_n}_{n \\geq 0} be a sequence of elements of Q_p^alg such that P(u_{n+1}) = u_n for all n \\geq 0. Let K_infty be the field generated over K by all the u_n. If K_infty / K is a Galois extension, then it is abelian, and our main result is that it is generated by the torsion points of a relative Lubin-Tate group (a generalization of the usual Lubin-Tate groups). 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