Galois groups and cohomological functors

Ido Efrat, Ján Mináč

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Let q = ps be a prime power, F a field containing a root of unity of order q, and GF its absolute Galois group. We determine a new canonical quotient Gal(F(3)/F) of GF which encodes the full mod-q cohomology ring H∗(GF, 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 Gal(E/F) is isomorphic to {1}, ℤ/p or to the nonabelian group Hp3 of order p3 and exponent p.

Original languageEnglish
Pages (from-to)2697-2720
Number of pages24
JournalTransactions of the American Mathematical Society
Volume369
Issue number4
DOIs
StatePublished - 1 Jan 2017

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Galois groups and cohomological functors'. Together they form a unique fingerprint.

Cite this