Imaginary quadratic fields with isomorphic abelian Galois groups
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Mathematical institute | |
| dc.contributor.author | ANGELAKIS, Athanasios | |
| hal.structure.identifier | Mathematical institute | |
| dc.contributor.author | STEVENHAGEN, Peter | |
| dc.contributor.editor | Everett W. Howe and Kiran S. Kedlaya | |
| dc.date.accessioned | 2024-04-04T02:24:15Z | |
| dc.date.available | 2024-04-04T02:24:15Z | |
| dc.date.created | 2012-09-26 | |
| dc.date.issued | 2013-11-14 | |
| dc.date.conference | 2012-07-09 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189800 | |
| dc.description.abstractEn | In 1976, Onabe discovered that, in contrast to the Neukirch-Uchida results that were proved around the same time, a number field $K$ is not completely characterized by its absolute abelian Galois group $A_K$. The first examples of non-isomorphic $K$ having isomorphic $A_K$ were obtained on the basis of a classification by Kubota of idele class character groups in terms of their infinite families of Ulm invariants, and did not yield a description of $A_K$. In this paper, we provide a direct 'computation' of the profinite group $A_K$ for imaginary quadratic $K$, and use it to obtain many different $K$ that all have the same minimal absolute abelian Galois group. | |
| dc.language.iso | en | |
| dc.publisher | Mathematical Sciences Publisher | |
| dc.subject.en | absolute Galois group | |
| dc.subject.en | class field theory | |
| dc.subject.en | group extensions | |
| dc.title.en | Imaginary quadratic fields with isomorphic abelian Galois groups | |
| dc.type | Communication dans un congrès | |
| dc.identifier.doi | 10.2140/obs.2013.1.21 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1209.6005 | |
| bordeaux.page | 21-39 | |
| bordeaux.volume | 1 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.conference.title | ANTS X - Tenth Algorithmic Number Theory Symposium | |
| bordeaux.country | US | |
| bordeaux.conference.city | San Diego | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00751883 | |
| hal.version | 1 | |
| hal.invited | non | |
| hal.proceedings | oui | |
| hal.conference.end | 2012-07-13 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00751883v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2013-11-14&rft.volume=1&rft.spage=21-39&rft.epage=21-39&rft.au=ANGELAKIS,%20Athanasios&STEVENHAGEN,%20Peter&rft.genre=unknown |
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