Arboreal representations, sectional monodromy groups, and abelian varieties over finite fields

This thesis consists of three independent parts. The first part studies arboreal representations of Galois groups - an arithmetic dynamics analogue of Tate modules - and proves some large image results, in particular confirming a conjecture of Odoni. Given a field K, a separable polynomial [mathematical expression], and an element [mathematical expression], the full backward orbit [mathematical expression] has a natural action of the Galois group [mathematical expression]. For a fixed [mathematical expression] with [mathematical expression] and for most choices of t, the orbit [mathematical expression] has the structure of complete rooted [mathematical expression]. The Galois action on [mathematical expression] thus defines a homomorphism [mathematical expression]. The map [mathematical expression] is the arboreal representation attached to f and t.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2020

Author dc:creator

• Kadets, Borys.

Advisor dc:contributor.advisor

• Bjorn Poonen.

• Mathematics.

Statement dc:rights

• MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/126927

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/126927