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# Classifying the image of the arboreal Galois representation

## Electronic Theses and Dissertations

### Item Details

abstract
Let $E$ be an elliptic curve without complex multiplication over a number field $F$, let $\ell$ be a prime, and let $\alpha\in E(F)$ be a point of infinite order such that $\alpha+T$ is not $\ell$ times a point over $F$ for any $F$-rational torsion point $T$. We prove that if we fix the image of the usual $\ell$-adic representation attached to $E$, $$\rho : \Gal(T_\infty/F)\rightarrow \Aut(T_\ell(E)),$$
subject
arithmetic dynamics
arithmetic geometry
elliptic curves
galois representations
contributor
Rouse, Jeremy A (committee chair)
Bourdon, Abbey (committee member)
Moore, Frank W. (committee member)
date
2019-05-24T08:35:46Z (accessioned)
2019-05-24T08:35:46Z (available)
2019 (issued)
degree
Mathematics and Statistics (discipline)
identifier
http://hdl.handle.net/10339/93959 (uri)
language
en (iso)
publisher
Wake Forest University
title
Classifying the image of the arboreal Galois representation
type
Thesis