Algebra & Number Theory

Kummer theory for Drinfeld modules

Richard Pink

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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.

Article information

Algebra Number Theory, Volume 10, Number 2 (2016), 215-234.

Received: 21 February 2012
Revised: 11 July 2012
Accepted: 5 November 2012
First available in Project Euclid: 16 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11G09: Drinfelʹd modules; higher-dimensional motives, etc. [See also 14L05]
Secondary: 11R58: Arithmetic theory of algebraic function fields [See also 14-XX]


Pink, Richard. Kummer theory for Drinfeld modules. Algebra Number Theory 10 (2016), no. 2, 215--234. doi:10.2140/ant.2016.10.215.

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