Potential Good Reduction of Degree 2 Rational Maps

dc.contributor.advisor Manes, Michelle
dc.contributor.author Yap, Diane
dc.date.accessioned 2013-02-06T20:14:23Z
dc.date.available 2013-02-06T20:14:23Z
dc.date.issued 2012
dc.description Thesis (Ph. D.)--University of Hawaii at Manoa, 2012.
dc.description.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.
dc.format.extent vii, 44 leaves
dc.identifier.uri http://hdl.handle.net/10125/25935
dc.language en-US
dc.publisher University of Hawaii at Manoa
dc.relation Theses for the degree of Doctor of Philosophy (University of Hawaii at Manoa). Mathematics; no. ????
dc.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.
dc.title Potential Good Reduction of Degree 2 Rational Maps
dc.type Thesis
dc.type.dcmi Text
local.thesis.degreelevel PhD
local.thesis.department Mathematics
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