Reflection theorem for divisor class groups of relative quadratic function fields

Abstract

We present the reflection theorem for divisor class groups of relative quadratic function fields. Let K be a global function field with constant field F q . Let L 1 be a quadratic geometric extension of K and let L 2 be its twist by the quadratic constant field extension of K. We show that for every odd integer m that divides q + 1 the divisor class groups of L 1 and L 2 have the same m-rank.