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From Frobenius Structures to Differential Equations

Matzat, B. Heinrich

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Abstract

Frobenius structures are omnipresent in arithmetic geometry. In this note we show that over suitable rings, Frobenius endomorphisms define differential structures and vice versa. This includes, for example, differential rings in positive characteristic and complete non-archimedean differential rings in characteristic zero. Further, in the global case, the existence of sufficiently many Frobenius rings is related to algebraicity properties. These results apply, for example, to t-motives as well as to p-adic and arithmetic differential equations.

Item Type: Preprint
Series Name: IWR-Preprints
Date Deposited: 06. Feb 2008 09:57
Date: 2008
Faculties / Institutes: Service facilities > Interdisciplinary Center for Scientific Computing
Subjects: 510 Mathematics
Controlled Keywords: Frobenius-Endomorphismus, Differentialgleichung, Frobenius-Ring, Differentialring
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