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367
Cyclic Cohomology of Étale Groupoids; The General Case
 Ktheory
, 1999
"... We give a general method for computing the cyclic cohomology of crossed products by 'etale groupoids, extending the FeiginTsyganNistor spectral sequences. In particular we extend the computations performed by Brylinski, Burghelea, Connes, Feigin, Karoubi, Nistor and Tsygan for the convolution alge ..."
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Cited by 21 (1 self)
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We give a general method for computing the cyclic cohomology of crossed products by 'etale groupoids, extending the FeiginTsyganNistor spectral sequences. In particular we extend the computations performed by Brylinski, Burghelea, Connes, Feigin, Karoubi, Nistor and Tsygan for the convolution algebra C 1 c (G) of an 'etale groupoid, removing the Hausdorffness condition and including the computation of hyperbolic components. Examples like group actions on manifolds and foliations are considered. Keywords: cyclic cohomology, groupoids, crossed products, duality, foliations. Contents 1 Introduction 3 2 Homology and Cohomology of Sheaves on ' Etale Groupoids 4 2.1 ' Etale Groupoids : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2.2 \Gamma c in the nonHausdorff case : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.3 Homology and Cohomology of ' Etale Groupoids : : : : : : : : : : : : : : : : : : : : : 8 3 Cyclic Homologies of Sheaves ...
A Koszul duality for props
 Trans. of Amer. Math. Soc
"... Abstract. The notion of prop models the operations with multiple inputs and multiple outputs, acting on some algebraic structures like the bialgebras or the Lie bialgebras. In this paper, we generalize the Koszul duality theory of associative algebras and operads to props. ..."
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Cited by 21 (4 self)
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Abstract. The notion of prop models the operations with multiple inputs and multiple outputs, acting on some algebraic structures like the bialgebras or the Lie bialgebras. In this paper, we generalize the Koszul duality theory of associative algebras and operads to props.
Derived categories, resolutions, and Brown representability
, 2004
"... These notes are based on a series of five lectures given during the ..."
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Cited by 20 (2 self)
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These notes are based on a series of five lectures given during the
Realizability Of Modules Over Tate Cohomology
, 2001
"... Let k be a eld and let G be a nite group. There is a canonical element in the Hochschild cohomology of the Tate cohomology G 2 HH 3; 1 ^ H (G; k) with the following property. Given a graded ^ H (G; k)module X, the image of G in Ext 3; 1 ^ H (G;k) (X; X) vanishes if and only if X is is ..."
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Cited by 20 (1 self)
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Let k be a eld and let G be a nite group. There is a canonical element in the Hochschild cohomology of the Tate cohomology G 2 HH 3; 1 ^ H (G; k) with the following property. Given a graded ^ H (G; k)module X, the image of G in Ext 3; 1 ^ H (G;k) (X; X) vanishes if and only if X is isomorphic to a direct summand of ^ H (G; M) for some kGmodule M . The description of the realizability obstruction works in any triangulated category with direct sums. We show that in the case of the derived category of a dierential graded algebra A, there is also a canonical element of Hochschild cohomology HH 3; 1 H (A) which is a predecessor for these obstructions.
Morita theory in abelian, derived and stable model categories, Structured ring spectra
 London Math. Soc. Lecture Note Ser
, 2004
"... These notes are based on lectures given at the Workshop on Structured ring spectra and ..."
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Cited by 19 (0 self)
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These notes are based on lectures given at the Workshop on Structured ring spectra and
Acyclicity Versus Total Acyclicity for Complexes over Noetherian Rings
 DOCUMENTA MATH.
, 2006
"... It is proved that for a commutative noetherian ring with dualizing complex the homotopy category of projective modules is ..."
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Cited by 18 (1 self)
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It is proved that for a commutative noetherian ring with dualizing complex the homotopy category of projective modules is
Semidualizing modules and related Gorenstein homological dimensions
 J. Pure Appl. Algebra
"... Abstract. A semidualizing module over a commutative noetherian ring A is a finitely generated module C with RHomA(C, C) ≃ A in the derived category D(A). We show how each such module gives rise to three new homological dimensions which we call C–Gorenstein projective, C–Gorenstein injective, and C ..."
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Cited by 18 (4 self)
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Abstract. A semidualizing module over a commutative noetherian ring A is a finitely generated module C with RHomA(C, C) ≃ A in the derived category D(A). We show how each such module gives rise to three new homological dimensions which we call C–Gorenstein projective, C–Gorenstein injective, and C–Gorenstein flat dimension, and investigate the properties of these dimensions.
Minimal Resolutions of Algebras
 J. Algebra
, 1999
"... . A method is described for constructing the minimal projective resolution of an algebra considered as a bimodule over itself. The method applies to an algebra presented as the quotient of a tensor algebra over a separable algebra by an ideal of relations which is either homogeneous or admissable (w ..."
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Cited by 17 (0 self)
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. A method is described for constructing the minimal projective resolution of an algebra considered as a bimodule over itself. The method applies to an algebra presented as the quotient of a tensor algebra over a separable algebra by an ideal of relations which is either homogeneous or admissable (with some additional finiteness restrictions in the latter case). In particular, it applies to any finite dimensional algebra over an algebraically closed field. The method is illustrated by a number of examples, viz. truncated algebras, monomial algebras and Koszul algebras, with the aim of unifying existing treatments of these in the literature. 1991 Mathematics Subject Classification. Primary: 16E99, 18G10. Secondary: 16D20, 16E40, 16G20, 16W50. 1. Introduction A projective resolution of an algebra , considered as a bimodule over itself, is fundamental in governing the homological properties of the algebra. Such a resolution may be used to compute Hochschild homology and cohomology, to ...
On the structure theory of the Iwasawa algebra of a padic Lie group
 J. Eur. Math. Soc
"... Abstract. This paper is motivated by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, Λ of a padic analytic group G. For G without any ptorsion element we prove that Λ is an Auslander regular ring. This ..."
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Cited by 16 (3 self)
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Abstract. This paper is motivated by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, Λ of a padic analytic group G. For G without any ptorsion element we prove that Λ is an Auslander regular ring. This result enables us to give a good definition of the notion of a pseudonull Λmodule. This is classical when G = Zk p for some integer k ≥ 1, but was previously unknown in the noncommutative case. Then the category of Λmodules up to pseudoisomorphisms is studied and we obtain a weak structure theorem for the Zptorsion part of a finitely generated Λmodule. We also prove a local duality theorem and a version of AuslanderBuchsbaum equality. The arithmetic applications to the Iwasawa theory of abelian varieties are published elsewhere.