Hypertranscendance et Groupes de Galois aux differences

Details Hypertranscendance et Groupes de Galois aux differences Hypertranscendance et Groupes de Galois aux differences

2006-09-22

arxiv.org/abs/math/0609646v2

Mathematics

Quantum Algebra

42 pages

Scientific paper

This paper deals with criteria of algebraic independence for the derivatives of solutions of rank one difference equations. The key idea consists in deriving from the commutativity of the differentiation and difference operators a sequence of iterated extensions of the original difference module, thereby setting the problem in the framework of difference Galois theory and finally reducing it to an exercise in linear algebra. The involved tannakian categories are neutral over non necessarily algebraically closed fields, and this leads us to study the behaviour of Galois groups under base field extensions.

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