Endomorphisms of n-dimensional projective space over function fields

Title: Endomorphisms of n-dimensional projective space over function fields
Identifier: d_2009_2013:da63def848f3:10031
identifier: 10103
Creator: Tepper, Michael Louis,
Contributor: Lucien Szpiro
Date: 2009
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: Let K = k(C) be the function field of a complete nonsingular curve C over an arbitrary field k. The main result states a morphism ϕ : PNK →PNK is isotrivial if and only if it has potential good reduction at all places v of K. This generalizes results of Benedetto for polynomial maps on P1K and Baker for arbitrary rational maps on P1K . There are two proofs given. The first uses algebraic geometry and more specifically, geometric invariant theory. It is new even in the case of P1K . The second proof, using non-archimedean analysis and dynamics, more directly generalizes proofs of Benedetto and Baker for the N = 1 case. In addition, two applications for the result are given.
Type: dissertation
Source: 2009_2013.csv
degree: Ph.D.
Program: Mathematics