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Lifting $D$-modules from positive to zero characteristic

2011; Société Mathématique de France; Volume: 139; Issue: 2 Linguagem: Inglês

10.24033/bsmf.2606

2102-622X

João Pedro P. dos Santos,

Polynomial and algebraic computation

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.