Open AccessUn théorème de comparaison entre les faisceaux d’opérateurs différentiels de Berthelot et de Mebkhout-Narváez-Macarro
Author(s) -
Christine Noot-Huyghe
Publication year - 2002
Publication title -
journal of algebraic geometry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.824
H-Index - 50
eISSN - 1534-7486
pISSN - 1056-3911
DOI - 10.1090/s1056-3911-02-00296-5
Subject(s) - algorithm , annotation , type (biology) , semantics (computer science) , computer science , artificial intelligence , mathematics , programming language , biology , ecology
In this paper, we compare in one particular case, the arithmetic D D -modules introduced by Berthelot and the arithmetic D D -modules introduced by Mebkhout and Narváez-Macarro. We prove that there exists an equivalence of categories of coherent D D -modules when you consider the arithmetic D D -modules introduced by Berthelot on a projective smooth formal scheme X \mathcal {X} , over some discrete valuation ring R R of mixed characteristics ( 0 , p ) (0,p) , that is endowed with an ample divisor, along which the coefficients of the differential operators are overconvergent. On the side of Mebkhout-Narváez-Macarro, you have to look at differential operators over a smooth, affine, weakly formal scheme over R R , whose p p -adic completion is the complementary of Z Z into X \mathcal {X} . The equivalence of categories is given in one direction by taking global sections of the D D -modules.