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453
The correct relatively stable category for idempotent modules ∗
, 708
"... We answer a question posed in [4], and demonstrate that in general Rickard modules in relatively stable categories are not idempotent modules even if one localizes with respect to a tensor ideal subcategory. We also show that there is a modification one can make so as to recover the idempotent behav ..."
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We answer a question posed in [4], and demonstrate that in general Rickard modules in relatively stable categories are not idempotent modules even if one localizes with respect to a tensor ideal subcategory. We also show that there is a modification one can make so as to recover the idempotent
The spectrum of prime ideals in tensor triangulated categories
 J. Reine Angew. Math
"... Abstract. We define the spectrum of a tensor triangulated category K as the set of socalled prime ideals, endowed with a suitable topology. In this very generality, the spectrum is the universal space in which one can define supports for objects of K. This construction is functorial with respect to ..."
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Cited by 68 (5 self)
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to all tensor triangulated functors. Several elementary properties of schemes hold for such spaces, e.g. the existence of generic points and some quasicompactness. Locally trivial morphisms are proved to be nilpotent. We establish in complete generality a classification of thick ⊗ideal subcategories
Decomposing Thick Subcategories Of The Stable Module Category
 Math. Ann
, 1999
"... . Let mod kG be the stable category of finitely generated modular representations of a finite group G over a field k. We prove a KrullSchmidt theorem for thick subcategories of modkG. It is shown that every thick tensorideal C of mod kG (i.e. a thick subcategory which is a tensor ideal) has a (usu ..."
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Cited by 15 (6 self)
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. Let mod kG be the stable category of finitely generated modular representations of a finite group G over a field k. We prove a KrullSchmidt theorem for thick subcategories of modkG. It is shown that every thick tensorideal C of mod kG (i.e. a thick subcategory which is a tensor ideal) has a
c © SpringerVerlag 1999 Decomposing thick subcategories
, 1998
"... Abstract. Let mod kG be the stable category of finitely generated modular representations of a finite group G over a field k. We prove a KrullRemakSchmidt theorem for thick subcategories of mod kG. It is shown that every thick tensorideal C ofmod kG (i.e. a thick subcategory which is a tensor id ..."
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Abstract. Let mod kG be the stable category of finitely generated modular representations of a finite group G over a field k. We prove a KrullRemakSchmidt theorem for thick subcategories of mod kG. It is shown that every thick tensorideal C ofmod kG (i.e. a thick subcategory which is a tensor
Πsupports for modules for finite group schemes
"... Abstract. We introduce the space Π(G) of equivalence classes of πpoints of a finite group scheme G, and associate a subspace Π(G)M to any Gmodule M. Our results extend to arbitrary finite group schemes G over arbitrary fields k of positive characteristic and to arbitrarily large Gmodules the basi ..."
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Cited by 26 (8 self)
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variety of a Gmodule M, the invariant M ↦ → Π(G)M satisfies good properties for all modules, thereby enabling us to determine the thick, tensorideal subcategories of the stable
Lagrangian subcategories and braided tensor equivalences of twisted quantum doubles of finite groups
 Comm. Math. Phys
"... Abstract. We classify Lagrangian subcategories of the representation category of a twisted quantum double D ω (G), where G is a finite group and ω is a 3cocycle on it. In view of results of [DGNO] this gives a complete description of all braided tensor equivalent pairs of twisted quantum doubles of ..."
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Cited by 18 (7 self)
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Abstract. We classify Lagrangian subcategories of the representation category of a twisted quantum double D ω (G), where G is a finite group and ω is a 3cocycle on it. In view of results of [DGNO] this gives a complete description of all braided tensor equivalent pairs of twisted quantum doubles
Nuclear and Trace Ideals in Tensored *Categories
, 1998
"... We generalize the notion of nuclear maps from functional analysis by defining nuclear ideals in tensored categories. The motivation for this study came from attempts to generalize the structure of the category of relations to handle what might be called "probabilistic relations". The comp ..."
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Cited by 37 (12 self)
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We generalize the notion of nuclear maps from functional analysis by defining nuclear ideals in tensored categories. The motivation for this study came from attempts to generalize the structure of the category of relations to handle what might be called "probabilistic relations
KrullSchmidt decompositions for thick subcategories
, 2005
"... Abstract. Following Krause [Kra99], we prove KrullSchmidt theorems for thick subcategories of various triangulated categories: derived categories of rings, noetherian stable homotopy categories, stable module categories over Hopf algebras, and the stable homotopy category of spectra. In all these c ..."
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Cited by 5 (1 self)
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Abstract. Following Krause [Kra99], we prove KrullSchmidt theorems for thick subcategories of various triangulated categories: derived categories of rings, noetherian stable homotopy categories, stable module categories over Hopf algebras, and the stable homotopy category of spectra. In all
QUOTIENT CLOSED SUBCATEGORIES OF QUIVER REPRESENTATIONS
"... Abstract. Let Q be a finite quiver without oriented cycles, and let k be an algebraically closed field. The main result in this paper is that there is a natural bijection between the elements in the associated Coxeter group WQ and the cofinite additive quotientclosed subcategories of the category o ..."
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Cited by 3 (1 self)
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of finite dimensional right modules over kQ. We prove this correpondence by linking these subcategories to certain ideals in the preprojective algebra associated to Q, which are also indexed by elements of WQ. 1.
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