A general theory of Andr\'e's solution algebras
Algebraic Geometry
2020-01-28 v1 Number Theory
Abstract
We extend Yves Andr\'e's theory of solution algebras in differential Galois theory to a general Tannakian context. As applications, we establish analogues of his correspondence between solution fields and observable subgroups of the Galois group for iterated differential equations in positive characteristic and for difference equations. The use of solution algebras in the difference algebraic context also allows a new approach to recent results of Philippon and Adamczewski--Faverjon in transcendence theory.
Keywords
Cite
@article{arxiv.2001.09337,
title = {A general theory of Andr\'e's solution algebras},
author = {Levente Nagy and Tamás Szamuely},
journal= {arXiv preprint arXiv:2001.09337},
year = {2020}
}
Comments
Final version, to appear in Annales de l'Institut Fourier