Dynamical Shafarevich results for rational maps

Title: Dynamical Shafarevich results for rational maps
Identifier: d_2009_2013:396ea4e8aff3:11825
identifier: 12456
Creator: Stout, Brian Justin,
Contributor: Calyton Petsche | Lucien Szpiro
Date: 2013
Language: English
Publisher: City University of New York.
Subject: Mathematics | Applied mathematics | Good reduction | Rational maps
Abstract: Given a number field K and a finite set S of places of K, this dissertation studies rational maps with prescribed good reduction at every place v ∉ S. The first result shows that the set of all quadratic rational maps with the standard notion of good reduction outside S is Zariski dense in the moduli space M2 . The second result shows that if the notion of good reduction is strengthened by requiring a double unramified fixed point structure or an unramified two cycle, then one obtains a non-Zariksi density statement. The next result proves the existence of global minimal models of endomorphisms on Pn defined over the fractional field of principal ideal domain. This result is used to prove the last main theorem---the finiteness of twists of a rational maps on Pn over K with good reduction outside S..
Type: dissertation
Source: 2009_2013.csv
degree: Ph.D.
Program: Mathematics