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Kronecker-Weber plus epsilon | | Greg W. Anderson
; | | Date: |
15 Mar 2001 | | Subject: | Number Theory | math.NT | | Abstract: | We say that a group is {em almost abelian} if every commutator is central and squares to the identity. Now let $G$ be the Galois group of the algebraic closure of the field $QQ$ of rational numbers in the field of complex numbers. Let $G^{ab+epsilon}$ be the quotient of $G$ universal for homomorphisms to almost abelian profinite groups and let $QQ^{ab+epsilon}/QQ$ be the corresponding Galois extension. We prove that $QQ^{ab+epsilon}$ is generated by the roots of unity, the fourth roots of the (rational) prime numbers and the square roots of certain sine-monomials. The inspiration for the paper came from recent studies of algebraic $Gamma$-monomials by P.~Das and by S.~Seo. This paper has appeared as Duke Math. J. 114 (2002) 439-475. | | Source: | arXiv, math.NT/0103241 | | Services: | Forum | Review | PDF | Favorites | |
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