Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gorenstein Homology and Finiteness Properties of Local (Co)homology   This thesis is comprised of three chapters. The first chapter deals with
bounded complexes of Gorenstein projective and Gorenstein injective modules.
Deploying methods of relative homological algebra, we approximate such
complexes with bounded complexes of projective and injective modules,
respectively. As an application, we investigate the Gorenstein version of the
New Intersection Theorem.
  The second chapter studies the notion of cofiniteness for modules and
complexes set forth by Hartshorne. Recruiting techniques of derived category,
we study this notion thoroughly, obtain novel results, and extend some of the
results to stable under specialization sets.
  The third chapter delves into the Greenlees-May Duality Theorem which is
widely thought of as a far-reaching generalization of the Grothendieck's Local
Duality Theorem. This theorem is not addressed in the literature as it merits
and its proof is indeed a tangled web in a series of scattered papers. By
carefully scrutinizing the requisite tools, we present a clear-cut
well-documented proof of this theorem.

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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: cs