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Lifting \(D\)-modules from positive to zero characteristic. (Relèvement de \(D\)-modules de caractéristique positive en caractéristique nulle.) (English. French summary) Zbl 1233.13009

Summary: We study liftings or deformations of \(D\)-modules (\(D\) is the ring of differential operators from EGA IV) from positive characteristic to characteristic zero using ideas of Matzat and Berthelot’s theory of arithmetic \(D\)-modules. We pay special attention to the growth of the differential Galois group of the liftings. We also apply formal deformation theory (following Schlessinger and Mazur) to analyze the space of all liftings of a given \(D\)-module in positive characteristic. At the end we compare the problems of deforming a \(D\)-module with the problem of deforming a representation of a naturally associated group scheme.

MSC:

13N10 Commutative rings of differential operators and their modules
12H05 Differential algebra
14L15 Group schemes
12H25 \(p\)-adic differential equations
14B12 Local deformation theory, Artin approximation, etc.
13D10 Deformations and infinitesimal methods in commutative ring theory
18B99 Special categories
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