Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Associated primes and cofiniteness of local cohomology modules   Let $\mathfrak{a}$ be an ideal of Noetherian ring $R$ and let $M$ be an
$R$-module such that $\mathrm{Ext}^i_R(R/\mathfrak{a},M)$ is finite $R$-module
for every $i$. If $s$ is the first integer such that the local cohomology
module $\mathrm{H}^s_\mathfrak{a}(M)$ is non $\mathfrak{a}$-cofinite, then we
show that $\mathrm{Hom}_{R}(R/\mathfrak{a}, \mathrm{H}^s_\mathfrak{a}(M))$ is
finite. Specially, the set of associated primes of
$\mathrm{H}^s_\mathfrak{a}(M)$ is finite.
  Next assume $(R,\mathfrak{m})$ is a local Noetherian ring and $M$ is a
finitely generated module. We study the last integer $n$ such that the local
cohomology module $\mathrm{H}^n_\mathfrak{a}(M)$ is not $\mathfrak{m}$-cofinite
and show that $n$ just depends on the support of $M$.

7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph