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DC Field | Value | Language |
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dc.contributor.author | Braunling, Oliver | - |
dc.contributor.author | HENRARD, Ruben | - |
dc.contributor.author | VAN ROOSMALEN, Adam-Christiaan | - |
dc.date.accessioned | 2024-05-06T07:01:00Z | - |
dc.date.available | 2024-05-06T07:01:00Z | - |
dc.date.issued | 2024 | - |
dc.date.submitted | 2024-04-26T09:12:40Z | - |
dc.identifier.citation | Journal of the Institute of Mathematics of Jussieu, | - |
dc.identifier.uri | http://hdl.handle.net/1942/42848 | - |
dc.description.abstract | Clausen a predit que le groupe des classes d'ideles de Chevalley d'un corps de nombres F apparait comme le premier K-groupe de la categorie des F-espaces vectoriels localement compacts. Cela s'est avere vrai, et se generalise meme aux groupes K superieurs dans un sens approprie. Nous remplacons F par une $\mathbb {Q}$ -algebre semi-simple, et obtenons le groupe des classes d'ideles noncommutatif de Frohlich de maniere analogue, modulo les elements de norme reduite une. Meme dans le cas du corps de nombres, notre preuve est plus simple que celle existante, et repose sur le theoreme de localisation pour des sous-categories percolees. Enfin, en utilisant la theorie des corps de classes, nous interpretons la loi de reciprocite d'Hilbert (ainsi qu'une variante noncommutative) en termes de nos resultats.Clausen predicted that Chevalley's idele class group of a number field F appears as the first K-group of the category of locally compact F-vector spaces. This has turned out to be true and even generalizes to the higher K-groups in a suitable sense. We replace F by a semisimple $\mathbb {Q}$ -algebra and obtain Frohlich's noncommutative idele class group in an analogous fashion, modulo the reduced norm one elements. Even in the number field case, our proof is simpler than the existing one and based on the localization theorem for percolating subcategories. Finally, using class field theory as input, we interpret Hilbert's reciprocity law (as well as a noncommutative variant) in terms of our results. | - |
dc.description.sponsorship | We thank P. Arndt, B. Chow, B. Kahn, U. Rehmann and A. Vishik for correspondence. Thanks go to the Oberwolfach Seminar on TC and arithmetic in October 2019. The last author gratefully acknowledges past support from FWO (12.M33.16N). We thank the anonymous referee for the encouraging report. | - |
dc.language.iso | en | - |
dc.publisher | CAMBRIDGE UNIV PRESS | - |
dc.rights | The Author(s), 2024. Published by Cambridge University Press. | - |
dc.subject.other | Locally compact modules | - |
dc.subject.other | K-theory | - |
dc.subject.other | exact category | - |
dc.subject.other | idele class group | - |
dc.subject.other | Hilbert symbol | - |
dc.title | A NONCOMMUTATIVE ANALOGUE OF CLAUSEN'S VIEW ON THE IDÈLE CLASS GROUP | - |
dc.type | Journal Contribution | - |
local.format.pages | 48 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | Braunling, O (corresponding author), Univ Autonoma Madrid, Math, Madrid 28049, Spain. | - |
dc.description.notes | oliver.braunling@gmail.com; ruben.henrard@uhasselt.be; | - |
dc.description.notes | ac.vanroosmalen@xjtlu.edu.cn | - |
local.publisher.place | EDINBURGH BLDG, SHAFTESBURY RD, CB2 8RU CAMBRIDGE, ENGLAND | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
local.bibliographicCitation.status | Early view | - |
dc.identifier.doi | 10.1017/S1474748024000100 | - |
dc.identifier.isi | 001195563900001 | - |
local.provider.type | wosris | - |
local.description.affiliation | [Braunling, Oliver] Univ Autonoma Madrid, Math, Madrid 28049, Spain. | - |
local.description.affiliation | [Henrard, Ruben] Univ Hasselt, Dept WNI, Campus Diepenbeek, B-3590 Diepenbeek, Belgium. | - |
local.description.affiliation | [van Roosmalen, Adam-Christiaan] Xian Jiaotong Liverpool Univ, Dept Pure Math, Suzhou 215123, Peoples R China. | - |
local.uhasselt.international | yes | - |
item.accessRights | Restricted Access | - |
item.contributor | Braunling, Oliver | - |
item.contributor | HENRARD, Ruben | - |
item.contributor | VAN ROOSMALEN, Adam-Christiaan | - |
item.fulltext | With Fulltext | - |
item.fullcitation | Braunling, Oliver; HENRARD, Ruben & VAN ROOSMALEN, Adam-Christiaan (2024) A NONCOMMUTATIVE ANALOGUE OF CLAUSEN'S VIEW ON THE IDÈLE CLASS GROUP. In: Journal of the Institute of Mathematics of Jussieu,. | - |
crisitem.journal.issn | 1474-7480 | - |
crisitem.journal.eissn | 1475-3030 | - |
Appears in Collections: | Research publications |
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a-noncommutative-analogue-of-clausens-view-on-the-idele-class-group.pdf Restricted Access | Early view | 580.04 kB | Adobe PDF | View/Open Request a copy |
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