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Potential Good Reduction of Degree 2 Rational Maps

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Item Summary

Title: Potential Good Reduction of Degree 2 Rational Maps
Authors: Yap, Diane
Advisor: Manes, Michelle
Issue Date: 2012
Publisher: University of Hawaii at Manoa
Abstract: We give a complete characterization of degree two rational maps on P1 with potential good reduction over local fields. We show this happens exactly when the map corresponds to an integral point in the moduli space M2. The proof includes an algorithm by which to conjugate any degree two rational map corresponding to an integral point in M2 into a map with unit resultant. The local fields result is used to solve the same problem for number fields with class number 1. Some additional results are given for degree 2 rational maps over Q. We also give a full description of post-critically finite maps in M2(Q), including the algorithm used to find them.
Description: Thesis (Ph. D.)--University of Hawaii at Manoa, 2012.
Pages/Duration: vii, 44 leaves
URI/DOI: http://hdl.handle.net/10125/25935
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
Ph.D. Dissertations- Mathematics Department



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