Epsilon extensions over global function fields

Abstract

Recently Anderson described explicitly the epsilon extension of the maximal abelian Q(ab) of the rational number field Q, which is the compositum of all subfield of C quadratic over Q(ab) and Galois over Q. We have given an analogous description of the epsilon extension of the maximal abelian extension of the rational function field over a finite field. In this paper we extend the theory of epsilon extensions partially to a global function field with a distinguished place. The new ingredient is that the base field may have non-trivial class group.