Iterative Differential Galois Theory in Positive Characteristic: A Model Theoretic Approach
Moreno, Javier A.
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/86901
Description
Title
Iterative Differential Galois Theory in Positive Characteristic: A Model Theoretic Approach
Author(s)
Moreno, Javier A.
Issue Date
2008
Doctoral Committee Chair(s)
Henson, C. Ward
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
This thesis introduces a natural extension of Kolchin's differential Galois theory to positive characteristic iterative differential fields, generalizing to the non-linear case the iterative Picard-Vessiot theory recently developed by Matzat and van der Put. Instead of taking an algebraic approach, we use the methods and framework provided by the model theory of iterative differential fields. After defining what we mean by a strongly normal extension of iterative differential fields, we prove that these extensions have good Galois theory and that a G-primitive element theorem holds. Then, making use of the basic theory of arc spaces of algebraic groups, we define iterative logarithmic equations, finally proving that our strongly normal extensions are Galois extensions for these equations.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
