Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On graded local cohomology modules defined by a pair of ideals   Let $R = \bigoplus_{n \in \mathbb{N}_{0}} R_{n}$ be a standard graded ring,
$M$ be a finite graded $R$-module and $J$ be a homogenous ideal of $R$. In this
paper we study the graded structure of the $i$-th local cohomology module of
$M$ defined by a pair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. More
precisely, we discuss finiteness property and vanishing of the graded
components $H^{i}_{R_{+},J}(M)_{n}$.
  Also, we study the Artinian property and tameness of certain submodules and
quotient modules of $H^{i}_{R_{+},J}(M)$.

7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph