Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized local cohomology modules and homological Gorenstein
  dimensions   Let \fa be an ideal of a commutative Noetherian ring R and M and N two
finitely generated R-modules. Let \cd_{\fa}(M,N) denote the supremum of the i's
such that H^i_{\fa}(M,N)\neq 0. First, by using the theory of Gorenstein
homological dimensions, we obtain several upper bounds for \cd_{\fa}(M,N).
Next, over a Cohen-Macaulay local ring (R,\fm), we show that
\cd_{\fm}(M,N)=\dim R-\grade(\Ann_RN,M), provided that either projective
dimension of M or injective dimension of N is finite. Finally, over such rings,
we establish an analogue of the Hartshorne-Lichtenbaum Vanishing Theorem in the
context of generalized local cohomology modules.

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The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
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The categories of this paper are: adap-org
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph