On the derived categories of coherent sheaves on some homogeneous spaces
type: Item
instance of: scholarly article
title: On the derived categories of coherent sheaves on some homogeneous spaces
zbMATH Open document ID: 0651.18008
DOI: 10.1007/BF01393744
published in: Inventiones Mathematicae
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143579
review text: We quote in part from the paper: The derived category of coherent sheaves on the projective space P n has been shown to be equivalent (as a triangulated category) to the homotopy category of finite complexes of sheaves, consisting of finite direct sums of \({\mathcal O}(-i),\) \(i=0,1,...,n\). For a preadditive category \({\mathcal A}\) the author forms a triangulated category Tr(\({\mathcal A})\) which is ``generated freely'' by \({\mathcal A}\). Its objects are finite complexes, consisting of finite formal direct sums of objects of \({\mathcal A}\), and morphisms are homotopy classes of morphisms of complexes. The author then represents in the form Tr(\({\mathcal A})\) the derived categories of coherent sheaves on flag varieties and quadrics, and also the derived categories of finite- dimensional representations of parabolic subgroups of GL(n,\({\mathbb{C}})\).
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14F20
Mathematics Subject Classification ID: 18G15
zbMATH DE Number: 4061472
zbMATH Keywords: derived category of coherent sheaves
zbMATH Keywords: triangulated category
zbMATH Keywords: homotopy classes of morphisms of complexes
zbMATH Keywords: flag varieties
zbMATH Keywords: quadrics
zbMATH Keywords: parabolic subgroups
author: Mikhail Kapranov
MaRDI profile type: Publication
cites work: Q3715233
cites work: Q4186467
cites work: Spinors in n Dimensions
cites work: Fibrés exceptionnels et suite spectrale de Beilinson généralisée sur \({\mathbb{P}}_ 2({\mathbb{C}})\)
cites work: Exceptional vector bundles on projective spaces
cites work: Q4143433
cites work: Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
cites work: ON THE DERIVED CATEGORY OF COHERENT SHEAVES ON GRASSMANN MANIFOLDS
cites work: The derived category of coherent sheaves on a quadric
cites work: Lie algebra cohomology and the generalized Borel-Weil theorem
cites work: Q3947818
cites work: Vector bundles on complex projective spaces
cites work: Koszul resolutions and the Steenrod algebra
cites work: K-theory of quadric hypersurfaces
cites work: Homology of Noetherian rings and local rings
cites work: Q5621786
cites work: The decomposition of stable homotopy
cites work: The Trace Map and Characteristic Classes for Coherent Sheaves
description: scientific article; zbMATH DE number 4061472