CYCLOTOMIC UNITS IN FUNCTION FIELDS

Abstract

Let k be a global function field over the finite field F(q) with a fixed place infinity of degree 1. Let K be a cyclic extension of degree dividing q - 1, in which infinity is totally ramified. For a certain abelian extension L of k containing K, there are two notions of the group of cyclotomic units arising from sign normalized rank 1 Drinfeld modules on k and on K. In this article we compare these two groups of cyclotomic units.