Vol. 10, No. 2, 2016

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Kummer theory for Drinfeld modules

Richard Pink

Vol. 10 (2016), No. 2, 215–234

Let ϕ be a Drinfeld A-module of characteristic p0 over a finitely generated field K. Previous articles determined the image of the absolute Galois group of K up to commensurability in its action on all prime-to-p0 torsion points of ϕ, or equivalently, on the prime-to-p0 adelic Tate module of ϕ. In this article we consider in addition a finitely generated torsion free A-submodule M of K for the action of A through ϕ. We determine the image of the absolute Galois group of K up to commensurability in its action on the prime-to-p0 division hull of M, or equivalently, on the extended prime-to-p0 adelic Tate module associated to ϕ and M.

Mathematical Subject Classification 2010
Primary: 11G09
Secondary: 11R58
Received: 21 February 2012
Revised: 11 July 2012
Accepted: 5 November 2012
Published: 16 March 2016
Richard Pink
Department of Mathematics
ETH Zürich
CH-8092 Zürich