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Finite Generation of Cohomology of Quotients of PBW AlgebrasShroff, Piyush 2012 August 1900 (has links)
In this dissertation we prove nite generation of the cohomology of quotients of a PBW algebra denoted by A by relating it to the cohomology of quotients of a quantum
symmetric algebra denoted by S which is isomorphic to the associated graded algebra of A. The proof uses a spectral sequence argument and a nite generation lemma adapted from Friedlander and Suslin.
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Ro(g)-graded equivariant cohomology theory and sheavesYang, Haibo 15 May 2009 (has links)
If G is a nite group and if X is a G-space, then a Bredon RO(G)-graded equivariantcohomology theory is dened on X. Furthermore, if X is a G-manifold, thereexists a natural Čech hypercohomology theory on X. While Bredon RO(G)-gradedcohomology is important in the theoretical aspects, the Čech cohomology is indispensablewhen computing the cohomology groups. The purpose of this dissertation is toconstruct an isomorphism between these two types of cohomology theories so that theinterplay becomes deeper between the theory and concretely computing cohomologygroups of classical objects. Also, with the aid of Čech cohomology, we can naturallyextend the Bredon cohomology to the more generalized Deligne cohomology.In order to construct such isomorphism, on one hand, we give a new constructionof Bredon RO(G)-graded equivariant cohomology theory from the sheaf-theoreticviewpoint. On the other hand, with Illman's theorem of smooth G-triangulation ofa G-manifold, we extend the existence of good covers from the nonequivariant tothe equivariant case. It follows that, associated to an equivariant good cover of aG-manifold X, there is a bounded spectral sequence converging to Čech hypercohomologywhose E1 page is isomorphic to the E1 page of a Segal spectral sequence whichconverges to the Bredon RO(G)-graded equivariant cohomology. Furthermore, Thisisomorphism is compatible with the structure maps in the two spectral sequences. So there is an induced isomorphism between two limiting objects, which are exactly theČech hypercohomology and the Bredon RO(G)-graded equivariant cohomology.We also apply the above results to real varieties and obtain a quasi-isomorphismbetween two commonly used complexes of presheaves.
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Ro(g)-graded equivariant cohomology theory and sheavesYang, Haibo 15 May 2009 (has links)
If G is a nite group and if X is a G-space, then a Bredon RO(G)-graded equivariantcohomology theory is dened on X. Furthermore, if X is a G-manifold, thereexists a natural Čech hypercohomology theory on X. While Bredon RO(G)-gradedcohomology is important in the theoretical aspects, the Čech cohomology is indispensablewhen computing the cohomology groups. The purpose of this dissertation is toconstruct an isomorphism between these two types of cohomology theories so that theinterplay becomes deeper between the theory and concretely computing cohomologygroups of classical objects. Also, with the aid of Čech cohomology, we can naturallyextend the Bredon cohomology to the more generalized Deligne cohomology.In order to construct such isomorphism, on one hand, we give a new constructionof Bredon RO(G)-graded equivariant cohomology theory from the sheaf-theoreticviewpoint. On the other hand, with Illman's theorem of smooth G-triangulation ofa G-manifold, we extend the existence of good covers from the nonequivariant tothe equivariant case. It follows that, associated to an equivariant good cover of aG-manifold X, there is a bounded spectral sequence converging to Čech hypercohomologywhose E1 page is isomorphic to the E1 page of a Segal spectral sequence whichconverges to the Bredon RO(G)-graded equivariant cohomology. Furthermore, Thisisomorphism is compatible with the structure maps in the two spectral sequences. So there is an induced isomorphism between two limiting objects, which are exactly theČech hypercohomology and the Bredon RO(G)-graded equivariant cohomology.We also apply the above results to real varieties and obtain a quasi-isomorphismbetween two commonly used complexes of presheaves.
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On strongly group-graded algebras and stably flat modulesAlcock, Edward January 2000 (has links)
No description available.
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Complete cohomological functors and finiteness conditionsNucinkis, Brita Erna Anita January 1996 (has links)
No description available.
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A (co)homology for restricted Lie algebrasDokas, I. January 2000 (has links)
No description available.
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The general linear group and the Bott spectral sequenceHammersley, Richard Paul January 1992 (has links)
No description available.
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Covering and sheaf theories on module categoriesSayer, Richard Michael Paul January 1998 (has links)
No description available.
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The cohomology of infinite soluble groupsKropholler, P. H. January 1984 (has links)
No description available.
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The geometry of complex orbifoldsWren, Andrew January 1994 (has links)
No description available.
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