Journal of Symbolic Logic

Iterative differential Galois theory in positive characteristic: A model theoretic approach

Javier Moreno

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Abstract

This paper 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. We use the methods and framework provided by the model theory of iterative differential fields. We offer a definition of strongly normal extension of iterative differential fields, and then prove that these extensions have good Galois theory and that a G-primitive element theorem holds. In addition, 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.

Article information

Source
J. Symbolic Logic, Volume 76, Issue 1 (2011), 125-142.

Dates
First available in Project Euclid: 4 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1294170992

Digital Object Identifier
doi:10.2178/jsl/1294170992

Mathematical Reviews number (MathSciNet)
MR2791340

Zentralblatt MATH identifier
1225.03041

Subjects
Primary: 03C98: Applications of model theory [See also 03C60]
Secondary: 12H05: Differential algebra [See also 13Nxx]

Citation

Moreno, Javier. Iterative differential Galois theory in positive characteristic: A model theoretic approach. J. Symbolic Logic 76 (2011), no. 1, 125--142. doi:10.2178/jsl/1294170992. https://projecteuclid.org/euclid.jsl/1294170992


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