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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Relations in the maximal pro-$ p$ quotients of absolute Galois groups


Authors: Ján Mináč, Michael Rogelstad and Nguyễn Duy Tân
Journal: Trans. Amer. Math. Soc. 373 (2020), 2499-2524
MSC (2010): Primary 12F10; Secondary 12E30, 20E18, 55S30
DOI: https://doi.org/10.1090/tran/8003
Published electronically: January 7, 2020
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Abstract: We observe that some fundamental constructions in Galois theory can be used to obtain interesting restrictions on the structure of Galois groups of maximal $ p$-extensions of fields containing a primitive $ p$-th root of unity. This is an extension of some significant ideas of Demushkin, Labute, and Serre from local fields to all fields containing a primitive $ p$-th root of unity. Our techniques use certain natural simple Galois extensions together with some considerations in Galois cohomology and Massey products.


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Additional Information

Ján Mináč
Affiliation: Department of Mathematics, Western University, London, Ontario, Canada N6A 5B7
Email: minac@uwo.ca

Michael Rogelstad
Affiliation: Department of Mathematics, Western University, London, Ontario, Canada N6A 5B7
Email: mrogelst@uwo.ca

Nguyễn Duy Tân
Affiliation: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307, Hanoi, Vietnam
Email: duytan@math.ac.vn

DOI: https://doi.org/10.1090/tran/8003
Received by editor(s): August 5, 2018
Received by editor(s) in revised form: February 26, 2019, and July 29, 2019
Published electronically: January 7, 2020
Additional Notes: The first-named author was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grant R0370A01.
The third-named author was partially supported by the Vietnam Academy of Science and Technology grant ĐLTE00.01/18-19.
Dedicated: Dedicated to John Labute
Article copyright: © Copyright 2019 American Mathematical Society