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Arboreal Galois Representations.

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Item Summary

Title:Arboreal Galois Representations.
Authors:Combs, TJ
Contributors:Mathematics (department)
Date Issued:Aug 2018
Publisher:University of Hawaiʻi at Mānoa
Abstract:We provide some general tools that can be used for polynomials in any degree to show G1 =
Aut(T1). We introduce the idea of Newton irreducibility to help push us closer to a proof to Odoni's
conjecture for monic integer polynomials when d = 4. We also show that current techniques used
in the literature will not work in proving Odoni's conjecture for monic quartic polynomials. Finally,
we look at how certain behaviors of the critical points of a polynomial f(x) 2 K[x] force G1 to
have in nite index in Aut(T1).
Description:Ph.D. Thesis. University of Hawaiʻi at Mānoa 2018.
URI:http://hdl.handle.net/10125/62524
Rights:All UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner.
Appears in Collections: Ph.D. - Mathematics


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