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On local cohomology and local homology based on an arbitrary supportSarria, Luis Alberto Alba 15 December 2015 (has links)
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Previous issue date: 2015-12-15 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work develops the theories of local cohomology and local homology with respect to
an arbitrary set of ideals and generalises most of the important results from the classical
theories. It also introduces the category of quasi-holonomic D-modules and proves some
finiteness properties of local cohomology modules which generalise Lyubeznik's results
in some sense. / Este trabalho desenvolve as teorias de cohomologia e homologia locais com respeito
a um conjunto arbitrário de ideais e generaliza vários dos resultados importantes das
teorias clássicas. Também, introduz a categoria dos D-módulos quase-holônomos e
prova alguns resultados de finitude de cohomologia local que generalizam, em algum
sentido, os resultados de G. Lyubeznik.
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