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 language | English |
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Pages (from-to) | 2697-2720 |
Number of pages | 24 |
Journal | Transactions of the American Mathematical Society |
Volume | 369 |
Issue number | 4 |
DOIs | |
State | Published - 1 Jan 2017 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics