Algebra & Number Theory

Kummer theory for Drinfeld modules

Richard Pink

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1510842479

Digital Object Identifier
doi:10.2140/ant.2016.10.215

Mathematical Reviews number (MathSciNet)
MR3477742

Zentralblatt MATH identifier
1382.11044

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

Citation

Pink, Richard. Kummer theory for Drinfeld modules. Algebra Number Theory 10 (2016), no. 2, 215--234. doi:10.2140/ant.2016.10.215. https://projecteuclid.org/euclid.ant/1510842479


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