Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohomological dimensions of specialization-closed subsets and
  subcategories of modules   Let R be a commutative noetherian ring. In this paper, we study
specialization-closed subsets of Spec R. More precisely, we first characterize
the specialization-closed subsets in terms of various closure properties of
subcategories of modules. Then, for each nonnegative integer n we introduce the
notion of n-wide subcategories of R-modules to consider the question asking
when a given specialization-closed subset has cohomological dimension at most
n.

4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph