Item Details

title

Classifying the image of the arboreal Galois representation

author

Cerchia, Michael

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

type

Thesis