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A classification of localizing subcategories by relative homological algebra

dc.contributor.advisorMeyer, Ralf Prof. Dr.
dc.contributor.authorNadareishvili, George
dc.titleA classification of localizing subcategories by relative homological algebrade
dc.contributor.refereeMeyer, Ralf Prof. Dr.
dc.description.abstractengIn this thesis, we use the tools of relative homological algebra in triangulated categories to define a sensible notion of support for objects in the bootstrap class of a Kasparov category of C*-algebras over a finite topological space with totally ordered lattice of open subsets. This category is equivalent to a bootstrap category of filtrations of C*-algebras. As a consequence, we provide a full classification of localizing subcategories of the bootstrap category in terms of a product of lattices of noncrossing partitions of a regular polygon. In addition, we consider the 2-periodic derived category of countable modules over the ring of upper triangular matrices. Since the homological algebra is the same, the lattices of localizing subcategories in this category and the bootstrap category are isomorphic. de
dc.contributor.coRefereeSchick, Thomas Prof. Dr.
dc.subject.engKasparov categoryde
dc.subject.enghomological algebrade
dc.subject.engtriangulated categoryde
dc.subject.engnon-commutative topologyde
dc.subject.engfiltrations of C*-algebrasde
dc.subject.engC*-algebras over a topological spacede
dc.subject.englocalizing subcategoryde
dc.subject.englocalising subcategoryde
dc.subject.engBivariant K-theoryde
dc.subject.engFiltrated K-theoryde
dc.subject.engrelative homological algebrade
dc.subject.engbootstrap classde
dc.subject.engring of upper triangular matricesde
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de

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