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Skew differential fields, differential and difference equations. (English) Zbl 1082.12005
Loday-Richaud, Michèle (ed.), Complex analysis, dynamical systems, summability of divergent series and Galois theories. I. Volume in honor of Jean-Pierre Ramis. Proceedings of the conference, Toulouse, France, September 22–26, 2003 held on the occasion of J.-P. Ramis’ 60th birthday. Paris: Société Mathématique de France (ISBN 2-85629-167-8/pbk). Astérisque 296, 191-205 (2004).
From the introduction: Rationality questions for differential modules and differential operators are strongly related to skew differential fields …. The present paper reviews these descent problems but now in the context of meromorphic differential equations. A remarkable family of examples is the result. Equally surprising is that descent does hold for meromorphic $$q$$-difference equations. …Finally, it is shown that descent does not hold for meromorphic ordinary difference equations.
For the entire collection see [Zbl 1061.00006].
Reviewer: Eduardo Liz (Vigo)

##### MSC:
 12H20 Abstract differential equations 34M99 Ordinary differential equations in the complex domain
##### Keywords:
Galois cohomology; descent; skew differential fields
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