Kummer theory for Drinfeld modules

Pink, Richard

doi:10.2140/ant.2016.10.215

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Kummer theory for Drinfeld modules

Richard Pink

Vol. 10 (2016), No. 2, 215–234

DOI: 10.2140/ant.2016.10.215

Abstract

Let $ϕ$ be a Drinfeld $A$ -module of characteristic $p_{0}$ 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- $p_{0}$ torsion points of $ϕ$ , or equivalently, on the prime-to- $p_{0}$ 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- $p_{0}$ division hull of $M$ , or equivalently, on the extended prime-to- $p_{0}$ adelic Tate module associated to $ϕ$ and $M$ .

Mathematical Subject Classification 2010

Primary: 11G09

Secondary: 11R58

Milestones

Received: 21 February 2012

Revised: 11 July 2012

Accepted: 5 November 2012

Published: 16 March 2016

Authors

Richard Pink
Department of Mathematics ETH Zürich CH-8092 Zürich Switzerland

Vol. 10, No. 2, 2016

Richard Pink

Abstract

Mathematical Subject Classification 2010

Milestones

Authors