\(D^\dagger (\infty)\)-affinité des schémas projectifs. (\(D^\dagger (\infty)\)-affinity of projective schemes.)
type: Item
instance of: scholarly article
title: \(D^\dagger (\infty)\)-affinité des schémas projectifs. (\(D^\dagger (\infty)\)-affinity of projective schemes.)
zbMATH Open document ID: 0910.14005
publication date: 1998-11-09T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75315
review text: Suppose \(X\) is a smooth projective \(p\)-adic formal scheme, \(U=X-D\) the complement of an ample divisor. Then Berthelot has defined a sheaf (on \(X)\) of overconvergent differential operators. Here it is shown that coherent modules over this sheaf satisfy the usual ``Theorem A'' and ``Theorem B''. Previously this was known for affine space (with its canonical compactification). The proof uses various filtrations and clever choices of integral models. At the end it is also shown that the category of coherent overconvergent \(D\)-modules is invariant under maps of compactifications \(f:(U,X) \to(U',X')\) with \(U=U'\).
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 14G20
zbMATH DE Number: 1220347
zbMATH Keywords: \(D^\dag (\infty)\)-modules
zbMATH Keywords: vanishing theorems for \(D\)-modules
zbMATH Keywords: \(p\)-adic coefficients
zbMATH Keywords: \(p\)-adic formal scheme
zbMATH Keywords: coherent overconvergent \(D\)-modules
author: Christine Noot-Huyghe
MaRDI profile type: Publication
OpenAlex ID: W2317246488
cites work: Q5592048
cites work: ${\scr D}$-modules arithmétiques. I. Opérateurs différentiels de niveau fini
cites work: Finiteness and cohomological purity in rigid cohomology (with an appendix by Aise Johan de Jong)
cites work: Q3784384
cites work: Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
cites work: Q4864331
cites work: Q4360116
cites work: Boyarsky principle and \(\mathcal D\)-modules
cites work: Q3349024
cites work: Formal cohomology. I
cites work: Q4053758
cites work: Q4866833
DOI: 10.5802/AIF.1643
published in: Annales de l’institut Fourier
reviewed by: Gerd Faltings
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description: scientific article; zbMATH DE number 1220347