Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

Un théorème de comparaison entre les faisceaux d'opérateurs différentiels de Berthelot et de Mebkhout-Narváez-Macarro


Author: Christine Noot-Huyghe
Journal: J. Algebraic Geom. 12 (2003), 147-199
DOI: https://doi.org/10.1090/S1056-3911-02-00296-5
Published electronically: August 26, 2002
MathSciNet review: 1948688
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Abstract | References | Additional Information

Abstract: In this paper, we compare in one particular case, the arithmetic $D$-modules introduced by Berthelot and the arithmetic $D$-modules introduced by Mebkhout and Narváez-Macarro. We prove that there exists an equivalence of categories of coherent $D$-modules when you consider the arithmetic $D$-modules introduced by Berthelot on a projective smooth formal scheme $\mathcal{X}$, over some discrete valuation ring $R$ of mixed characteristics $(0,p)$, 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 $R$, whose $p$-adic completion is the complementary of $Z$ into $\mathcal{X}$. The equivalence of categories is given in one direction by taking global sections of the $D$-modules.


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Additional Information

Christine Noot-Huyghe
Affiliation: UFR de mathématiques, Université de Rennes 1, campus de Beaulieu, 35042 Rennes cedex, France
Email: Christine.Huyghe@univ-rennes1.fr

DOI: https://doi.org/10.1090/S1056-3911-02-00296-5
Received by editor(s): September 8, 2000
Published electronically: August 26, 2002
Additional Notes: Pendant la préparation de cet article, l’auteur a bénéficié du soutien du programme TMR de la Communauté Européenne, dans le cadre du réseau Arithmetic Algebraic Geometry (Contrat ERBFMRXCT 960006).

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
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