Kronecker-Weber plus epsilon

الأصل · EN

We say that a group is 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 of rational numbers in the field of complex numbers. Let G+ε be the quotient of G universal for homomorphisms to almost abelian profinite groups and let +ε/ be the corresponding Galois extension. We prove that +ε 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 Γ-monomials by P. Das and by S. Seo. This paper has appeared as Duke Math. J. 114 (2002) 439-475.