## Algebra & Number Theory

### Kummer theory for Drinfeld modules

Richard Pink

#### 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
Revised: 11 July 2012
Accepted: 5 November 2012
First available in Project Euclid: 16 November 2017

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

#### 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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