We extend Yves André’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.

A general theory of André’s solution algebras

Szamuely, Tamás
Co-primo
2020-01-01

Abstract

We extend Yves André’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.
2020
Nagy, Levente; Szamuely, Tamás
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1078580
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