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Russian Mathematical Surveys, 2015, Volume 70, Issue 1, Pages 83–112
DOI: https://doi.org/10.1070/RM2015v070n01ABEH004937 (Mi rm9649) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Division algebras with the same maximal subfields

V. I. Chernousova, A. S. Rapinchukb, I. A. Rapinchukc

a University of Alberta, Edmonton, Canada
b University of Virginia, Charlottesville, USA
c Harvard University, Cambridge, USA
English version PDF (719 kB) Citations (11)
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DOI: https://doi.org/10.1070/RM2015v070n01ABEH004937
Abstract: This is a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. Also discussed are various generalizations of this problem and some of its applications. In the last section the problem is extended to the context of absolutely almost simple algebraic groups.
Bibliography: 51 titles.
Keywords: division algebra, unramified Brauer group, semisimple algebraic groups.
Funding agency Grant number
Canada Research Chair
Natural Sciences and Engineering Research Council of Canada (NSERC)
National Science Foundation DMS-1301800
United States - Israel Binational Science Foundation (BSF) 201049
Alexander von Humboldt-Stiftung
The first author was supported by the Canada Research Chair Program and by an NSERC research grant. The second author was partially supported by NSF grant DMS-1301800, BSF grant 201049, and the Humboldt Foundation. The third author was supported by an NSF Postdoctoral Fellowship. Part of this article was written during the Joint IMU-AMS meeting in Israel in June 2014, and the warm reception of Bar-Ilan and Tel Aviv Universities hosting the meeting is thankfully acknowledged.
Received: 09.09.2014
Russian version:
Uspekhi Matematicheskikh Nauk, 2015, Volume 70, Issue 1(421), Pages 89–122
DOI: https://doi.org/10.4213/rm9649
Bibliographic databases:
Document Type: Article
UDC: 512.552
MSC: 11R52, 12E15, 20G15
Language: English
Original paper language: Russian
Citation: V. I. Chernousov, A. S. Rapinchuk, I. A. Rapinchuk, “Division algebras with the same maximal subfields”, Uspekhi Mat. Nauk, 70:1(421) (2015), 89–122; Russian Math. Surveys, 70:1 (2015), 83–112
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:56
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