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The relative duality theorem for arithmetic \({\mathcal D}\)-modules. (Théorème de dualité relative pour les \({\mathcal D}\)-modules arithmétiques.) (French) Zbl 0876.14011
Summary: Let \({\mathcal D}\) be one of the rings of differential operators defined by P. Berthelot [Ann. Sci. Éc. Norm. Supér., IV. Sér. 29, No. 2, 185-272 (1996)] on a smooth scheme of unequal characteristics. We establish that the relative duality theorem for proper morphisms still holds in this context. More precisely we show that the direct image functor for \({\mathcal D}\)-modules commutes with the duality functor [see also A. Virrion, C. R. Acad. Sci., Paris, Sér. I 319, No. 12, 1283-1286 (1994; Zbl 0829.14010)].

14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
14G20 Local ground fields in algebraic geometry
13N10 Commutative rings of differential operators and their modules