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308
CLASSIFYING THICK SUBCATEGORIES OF PERFECT COMPLEXES
, 2006
"... Given a commutative coherent ring R, a bijective correspondence between the thick subcategories of perfect complexes Dper(R) and the Serre subcategories of finitely presented modules is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the set of (i ..."
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Given a commutative coherent ring R, a bijective correspondence between the thick subcategories of perfect complexes Dper(R) and the Serre subcategories of finitely presented modules is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the set
Classifying Serre subcategories of finitely presented modules
 Proc. Amer. Math. Soc
"... Abstract. Given a commutative coherent ring R, a bijective correspondence between the thick subcategories of perfect complexes Dper(R) and the Serre subcategories of finitely presented modules is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the s ..."
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Cited by 12 (4 self)
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Abstract. Given a commutative coherent ring R, a bijective correspondence between the thick subcategories of perfect complexes Dper(R) and the Serre subcategories of finitely presented modules is established. To construct this correspondence, properties of the Ziegler and Zariski topologies
Refining thick subcategory theorems
 Fundamenta Mathematicae
"... Abstract. We use a Ktheory recipe of Thomason to obtain classifications of triangulated subcategories via refining some standard thick subcategory theorems. We apply this recipe to the full subcategories of finite objects in the derived categories of rings and the stable homotopy category of spectr ..."
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Cited by 3 (3 self)
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of spectra. This gives, in the derived categories, a complete classification of the triangulated subcategories of perfect complexes over some noetherian rings. In the homotopy category of spectra we obtain only a partial classification of the triangulated subcategories of the finite plocal spectra. We use
Thick subcategories of the . . .
"... We classify thick subcategories of the bounded derived category of an abelian category A in terms of subcategories of A. The proof can be applied to characterize the localizing subcategories of the full derived category of A. As an application we prove an algebraic analogon of the telescope conject ..."
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We classify thick subcategories of the bounded derived category of an abelian category A in terms of subcategories of A. The proof can be applied to characterize the localizing subcategories of the full derived category of A. As an application we prove an algebraic analogon of the telescope
CLASSIFYING SUBCATEGORIES OF MODULES OVER A COMMUTATIVE NOETHERIAN RING
, 2008
"... Let R be a quotient ring of a commutative coherent regular ring by a finitely generated ideal. Hovey gave a bijection between the set of coherent subcategories of the category of finitely presented Rmodules and the set of thick subcategories of the derived category of perfect Rcomplexes. Using t ..."
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Cited by 11 (3 self)
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Let R be a quotient ring of a commutative coherent regular ring by a finitely generated ideal. Hovey gave a bijection between the set of coherent subcategories of the category of finitely presented Rmodules and the set of thick subcategories of the derived category of perfect Rcomplexes. Using
Classifying thick subcategories of the stable category of CohenMacaulay modules
, 2009
"... Various classification theorems of thick subcategories of a triangulated category have been obtained in many areas of mathematics. In this paper, as a higher dimensional version of the classification theorem of thick subcategories of the stable category of finitely generated representations of a fin ..."
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Cited by 23 (7 self)
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finite pgroup due to Benson, Carlson and Rickard, we consider classifying thick subcategories of the stable category of CohenMacaulay modules over a Gorenstein local ring. The main result of this paper yields a complete classification of the thick subcategories of the stable category of Cohen
Inferring Global Perceptual Contours from Local Features
, 1996
"... Introduction Computer vision can greatly benefit from perceptual grouping. Perceptual Grouping can be classified as a midlevel process directed toward closing the gap between what is produced by stateoftheart lowlevel algorithms (such as edge detectors) and what is desired as input to high lev ..."
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Cited by 210 (10 self)
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possible subsets for grouping (a complexity of O(2 #_of_points ), but the actual measurement of compatibility of a subset is not well defined. Methods for edge labeling (such as [4,27]) assume perfect segmentation and connectivity, and define constraints which are only valid under these assumptions
Thick subcategories of modules over commutative rings
, 2007
"... For a commutative noetherian ring A, we compare the support of a complex of Amodules with the support of its cohomology. This leads to a classification of all full subcategories of Amodules which are thick (that is, closed under taking kernels, cokernels, and extensions) and closed under taking ..."
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Cited by 11 (1 self)
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For a commutative noetherian ring A, we compare the support of a complex of Amodules with the support of its cohomology. This leads to a classification of all full subcategories of Amodules which are thick (that is, closed under taking kernels, cokernels, and extensions) and closed under taking
CLASSIFYING SUBCATEGORIES OF MODULES OVER A PID.
, 2006
"... Abstract. Let R be a commutative ring. A full additive subcategory C of Rmodules is triangulated if whenever two terms of a short exact sequence belong to C, then so does the third term. In this note we give a classification of triangulated subcategories of finitely generated modules over a princip ..."
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principal ideal domain. As a corollary we show that in the category of finitely generated modules over a PID, thick subcategories (triangulated subcategories closed under direct summands), wide subcategories (abelian subcategories closed under extensions) and Serre subcategories (wide subcategories closed
Stably thick subcategories of modules over Hopf algebras
 MATH. PROC. CAMBRIDGE PHILOS. SOC
, 2000
"... We discuss a general method for classifying certain subcategories of the category of finitedimensional modules over a finitedimensional cocommutative Hopf algebra B. Our method is based on that of BensonCarlsonRickard [BCR96], who classify such subcategories when B = kG, the group ring of a fin ..."
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Cited by 6 (1 self)
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We discuss a general method for classifying certain subcategories of the category of finitedimensional modules over a finitedimensional cocommutative Hopf algebra B. Our method is based on that of BensonCarlsonRickard [BCR96], who classify such subcategories when B = kG, the group ring of a
Results 1  10
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308