Galois groups and cohomological functors
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- by Ido Efrat and Ján Mináč PDF
- Trans. Amer. Math. Soc. 369 (2017), 2697-2720 Request permission
Abstract:
Let $q=p^s$ be a prime power, $F$ a field containing a root of unity of order $q$, and $G_F$ its absolute Galois group. We determine a new canonical quotient $\mathrm {Gal}(F_{(3)}/F)$ of $G_F$ which encodes the full mod-$q$ cohomology ring $H^*(G_F,\mathbb {Z}/q)$ and is minimal with respect to this property. We prove some fundamental structure theorems related to these quotients. In particular, it is shown that when $q=p$ is an odd prime, $F_{(3)}$ is the compositum of all Galois extensions $E$ of $F$ such that $\mathrm {Gal}(E/F)$ is isomorphic to $\{1\}$, $\mathbb {Z}/p$ or to the nonabelian group $H_{p^3}$ of order $p^3$ and exponent $p$.References
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Additional Information
- Ido Efrat
- Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, Be’er-Sheva 84105, Israel
- Email: efrat@math.bgu.ac.il
- Ján Mináč
- Affiliation: Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada
- Email: minac@uwo.ca
- Received by editor(s): August 12, 2013
- Received by editor(s) in revised form: February 15, 2015, and April 18, 2015
- Published electronically: July 29, 2016
- Additional Notes: The first author was supported by the Israel Science Foundation (grants No. 23/09 and 152/13)
The second author was supported in part by National Sciences and Engineering Council of Canada grant R0370A01. - © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 2697-2720
- MSC (2010): Primary 12G05, 12E30
- DOI: https://doi.org/10.1090/tran/6724
- MathSciNet review: 3592525