Embedded Picard-Vessiot extensions
Algebraic Geometry
2017-09-04 v1 Logic
Abstract
We prove that if T is a theory of large, bounded, fields of characteristic zero, with almost quantifier elimination, and T_D is the model companion of T + "D is a derivation", then for any model U of T_D, and differential subfield K of U whose field of constants is a model of T, and linear differential equation DY = AY over K, there is a Picard-Vessiot extension L of K for the equation which is embedded in U over K Likewise for logarithmic differential equations over K on connected algebraic groups over the constants of K and the corresponding strongly normal extensions of K.
Keywords
Cite
@article{arxiv.1709.00046,
title = {Embedded Picard-Vessiot extensions},
author = {Quentin Brouette and Greg Cousins and Anand Pillay and Francoise Point},
journal= {arXiv preprint arXiv:1709.00046},
year = {2017}
}
Comments
12 pages