The 2-Ideal Class Groups of ℚ(ζl)
For prime l we study the structure of the 2-part of the ideal class group Cl of ℚ(ζ l ). We prove that Cl ⊗ ℤ2) is a cyclic Galois module for all l < 10000 with one exception and compute the explicit structure in several cases.
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| Published in | Nagoya mathematical journal Vol. 162; pp. 1 - 18 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.06.2001
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| Subjects | |
| Online Access | Get full text |
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| Abstract | For prime l we study the structure of the 2-part of the ideal class group Cl of ℚ(ζ
l
). We prove that Cl ⊗ ℤ2) is a cyclic Galois module for all l < 10000 with one exception and compute the explicit structure in several cases. |
|---|---|
| AbstractList | For prime l we study the structure of the 2-part of the ideal class group Cl of ℚ(ζ
l
). We prove that Cl ⊗ ℤ2) is a cyclic Galois module for all l < 10000 with one exception and compute the explicit structure in several cases. For prime l we study the structure of the 2-part of the ideal class group Cl of ℚ(ζ l ). We prove that Cl ⊗ ℤ 2 ) is a cyclic Galois module for all l < 10000 with one exception and compute the explicit structure in several cases. |
| Author | Cornacchia, Pietro |
| Author_xml | – sequence: 1 givenname: Pietro surname: Cornacchia fullname: Cornacchia, Pietro email: cornac@dm.unipi.it organization: Corso XXV Aprile 60, 14100 Asti, Italy, cornac@dm.unipi.it |
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| CitedBy_id | crossref_primary_10_1017_nmj_2018_42 crossref_primary_10_5036_mjiu_50_15 |
| Cites_doi | 10.1006/jnth.1995.1084 10.1090/S0002-9939-97-03909-9 10.5802/aif.1299 10.24033/bsmf.1828 10.1090/S0025-5718-02-01432-1 10.1007/978-1-4612-0987-4 10.1006/jnth.1998.2300 10.1007/BF01388983 10.1090/S0025-5718-98-00939-9 10.24033/bsmf.1876 10.1142/0663 10.1007/978-1-4612-1934-7 10.5802/aif.1319 10.1006/jnth.1997.2184 |
| ContentType | Journal Article |
| Copyright | Copyright © Editorial Board of Nagoya Mathematical Journal 2001 |
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| References | S0027763000007777_ref4 S0027763000007777_ref11 S0027763000007777_ref12 S0027763000007777_ref5 S0027763000007777_ref13 S0027763000007777_ref6 S0027763000007777_ref7 S0027763000007777_ref15 Berthier (S0027763000007777_ref1) 1994 S0027763000007777_ref2 S0027763000007777_ref17 S0027763000007777_ref3 S0027763000007777_ref18 Gras (S0027763000007777_ref8) 1975; 277 S0027763000007777_ref10 Schoof (S0027763000007777_ref16) 1988–89 Rubin (S0027763000007777_ref14) S0027763000007777_ref9 |
| References_xml | – volume: 277 start-page: 89 year: 1975 ident: S0027763000007777_ref8 article-title: Méthodes et algorithmes pour le calcul numérique du nombre de classes et des unités des extensions cubiques cycliques de Q publication-title: J. Reine Angew. Math contributor: fullname: Gras – ident: S0027763000007777_ref10 doi: 10.1006/jnth.1995.1084 – ident: S0027763000007777_ref14 publication-title: The Main Conjecture contributor: fullname: Rubin – ident: S0027763000007777_ref3 doi: 10.1090/S0002-9939-97-03909-9 – ident: S0027763000007777_ref9 doi: 10.5802/aif.1299 – ident: S0027763000007777_ref12 doi: 10.24033/bsmf.1828 – ident: S0027763000007777_ref17 doi: 10.1090/S0025-5718-02-01432-1 – ident: S0027763000007777_ref11 doi: 10.1007/978-1-4612-0987-4 – year: 1994 ident: S0027763000007777_ref1 publication-title: Générateurs et structure du groupe des classes d’idéaux des corps denombres abéliens contributor: fullname: Berthier – ident: S0027763000007777_ref5 doi: 10.1006/jnth.1998.2300 – ident: S0027763000007777_ref13 doi: 10.1007/BF01388983 – ident: S0027763000007777_ref15 doi: 10.1090/S0025-5718-98-00939-9 – ident: S0027763000007777_ref6 doi: 10.24033/bsmf.1876 – ident: S0027763000007777_ref2 doi: 10.1142/0663 – ident: S0027763000007777_ref18 doi: 10.1007/978-1-4612-1934-7 – start-page: 185 year: 1988–89 ident: S0027763000007777_ref16 article-title: The structure of the minus class groups of abelian number fields publication-title: Séminaire de Théorie des Nombres contributor: fullname: Schoof – ident: S0027763000007777_ref7 doi: 10.5802/aif.1319 – ident: S0027763000007777_ref4 doi: 10.1006/jnth.1997.2184 |
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| Snippet | For prime l we study the structure of the 2-part of the ideal class group Cl of ℚ(ζ
l
). We prove that Cl ⊗ ℤ2) is a cyclic Galois module for all l < 10000... For prime l we study the structure of the 2-part of the ideal class group Cl of ℚ(ζ l ). We prove that Cl ⊗ ℤ 2 ) is a cyclic Galois module for all l < 10000... |
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| Title | The 2-Ideal Class Groups of ℚ(ζl) |
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