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Iterative Differential Equations and Finite Groups

Matzat, Bernd Heinrich

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It is an old question to characterize those differential equations or differential modules, respectively, whose solution spaces consist of functions which are algebraic over the base field. The most famous conjecture in this context is due to A. Gorthendieck and relates the algebraicity property with the p-curvature which apprears as the first integrability obstruction in characteristic p. Here we prove a variant of Grothendieck's conjecture for differential modules with vanishing higher integrability obstructions modulo p - these are iterative differential modules - and give some applications.

Item Type: Preprint
Series Name: IWR-Preprints
Date Deposited: 04 Dec 2006 06:56
Date: 2006
Faculties / Institutes: Service facilities > Interdisciplinary Center for Scientific Computing
Subjects: 510 Mathematics
Controlled Keywords: Algebraische Differentialgleichung/Endliche Gruppen
Uncontrolled Keywords: Iterative Differentialgleichung , Iteratives Differentialmodul
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