Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

Groupe de Brauer non ramifié de quotients par un groupe fini


Author: J.-L. Colliot-Thélène
Journal: Proc. Amer. Math. Soc. 142 (2014), 1457-1469
MSC (2010): Primary 12G05, 14E08, 14F22, 14M20
DOI: https://doi.org/10.1090/S0002-9939-2014-11855-7
Published electronically: February 6, 2014
MathSciNet review: 3168454
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Soit $ k$ un corps, $ G$ un groupe fini, $ G \hookrightarrow SL_{n,k}$ un plongement. Pour $ k$ algébriquement clos, Bogomolov a donné une formule pour le groupe de Brauer non ramifié du quotient $ SL_{n,k}/G$. On examine ce que donne sa méthode sur un corps $ k$ quelconque (de caractéristique nulle). Par cette méthode purement algébrique, on retrouve et étend des résultats obtenus au moyen de méthodes arithmétiques par Harari et par Demarche, comme la tri-
vialité du groupe de Brauer non ramifié pour $ k=\mathbf {Q}$ et $ G$ d'ordre impair.

[Let $ k$ be a field, $ G$ a finite group, $ G \hookrightarrow SL_{n,k}$ an embedding. For $ k$ an algebraically closed field, Bogomolov gave a formula for the unramified Brauer group of the quotient $ SL_{n,k}/G$. We develop his method over any characteristic zero field. This purely algebraic method enables us to recover and generalize results of Harari and of Demarche over number fields, such as the triviality of the unramified Brauer group for $ k=\mathbf {Q}$ and $ G$ of odd order.]


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 12G05, 14E08, 14F22, 14M20

Retrieve articles in all journals with MSC (2010): 12G05, 14E08, 14F22, 14M20


Additional Information

J.-L. Colliot-Thélène
Affiliation: CNRS, Université Paris-Sud Département de mathématiques, Bâtiment 425 91405 Orsay Cedex France
Email: jlct@math.u-psud.fr

DOI: https://doi.org/10.1090/S0002-9939-2014-11855-7
Received by editor(s): January 25, 2012
Received by editor(s) in revised form: March 23, 2012, April 17, 2012, May 7, 2012, and May 11, 2012
Published electronically: February 6, 2014
Communicated by: Lev Borisov
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.