Journal ArticleDOI
Thick subcategories of modules over commutative noetherian rings (with an appendix by Srikanth Iyengar)
TLDR
For a commutative noetherian ring A, the authors in this paper compare the support of a complex of A-modules with its cohomology, which leads to a classification of all full subcategories of A -modules which are thick (i.e., closed under taking kernels, cokernels, and extensions) and open under taking arbitrary direct sums.Abstract:
For a commutative noetherian ring A, we compare the support of a complex of A-modules with the support of its cohomology. This leads to a classification of all full subcategories of A-modules which are thick (that is, closed under taking kernels, cokernels, and extensions) and closed under taking arbitrary direct sums. In addition, subcategories of A-modules that are closed under taking submodules, extensions, and direct unions are classified via associated prime ideals.read more
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Local cohomology and support for triangulated categories
TL;DR: In this article, the authors propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small co-products, based on a construction of local cohomology func- tors on triangulation categories, with respect to a central ring of operators.
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Local cohomology and support for triangulated categories
TL;DR: In this paper, a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts is proposed, based on a construction of local cohomology functors on triangulation categories, with respect to a central ring of operators.
Journal ArticleDOI
Classifying thick subcategories of the stable category of Cohen–Macaulay modules
TL;DR: In this article, a higher-dimensional version of the classification theorem of thick subcategories of the stable category of finitely generated representations of a finite p-group due to Benson, Carlson and Rickard is presented.
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The Catalan combinatorics of the hereditary artin algebras
TL;DR: In this paper, a survey on the categorisation of the poset of generalized non-crossing partitions, using the representation theory of a hereditary artin algebra H, looking at the set P of exceptional subcategories in mod H is presented.
Journal ArticleDOI
Classification of Resolving Subcategories and Grade Consistent Functions
TL;DR: In this paper, the authors classify certain resolving subcategories of finitely generated modules over a commutative noetherian ring R by using integer-valued functions on Spec R.
References
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Des catégories abéliennes
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Resolutions of unbounded complexes
TL;DR: In this article, various types of resolutions of unbounded complexes of sheaves are constructed, with properties analogous to injectivity, flatness, flabbiness, etc. They are used to remove some boundedness conditions for the existence of the derived functors of functors such as Hom, tensor product, sections over an open subset, inverse and direct images, and for the validity of various formulae involving these derived functor.
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Homotopy limits in triangulated categories
Marcel Bökstedt,Amnon Neeman +1 more
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the stable derived category of a noetherian scheme
TL;DR: In this paper, the stable derived category of coherent sheaves is introduced for a noetherian scheme, and its applications include an analogue of maximal cohen-macaulay approximations, a construction of tate cohomology, and an extension of the classical Grothendieck duality.
Journal ArticleDOI
The chromatic tower for D(R)
Amnon Neeman,Marcel Bökstedt +1 more
TL;DR: In this paper, the triangulated subcategories of D*(R) epaisse are called triangulations if they are full and closed under direct summands.