Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstruction from Koszul homology and applications to module and
  derived categories   Let R be a commutative noetherian ring. Let M be a finitely generated
R-module. In this paper, we reconstruct M from its Koszul homology with respect
to a suitable sequence of elements of R by taking direct summands, syzygies and
extensions, and count the number of those operations. Using this result, we
consider generation and classification of certain subcategories of the category
of finitely generated R-modules, its bounded derived category and the
singularity category of R.

18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an