Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hartshorne's questions and weakly cofiniteness   Let $R$ be a commutative Noetherian ring, $\fa$ be an ideal of $R$ and $M$ be
an $R$-module. The main purpose of this paper is to answer the Hartshorn's
questions in the class of weakly Laskerian modules. It is shown that if $s\geq
1$ is a positive integer such that $\Ext^j_R(R/\fa, M)$ is weakly Laskerian for
all $j\leq s$ and the $R$-module $H^i_\fa(M)$ is $FD_{\leq 1}$ for all $i < s$,
then the $R$-module $H^i_\fa(M)$ is $\fa$-weakly cofinite for all $i <s$. In
addition, we show that the category of all $\fa$-weakly cofinite $FD_{\leq 1}$
$R$-modules is an Abelian subcategory of the category of all $R$-modules. Also,
we prove that if $\Ext^i_R(R/\fa,M)$ is weakly Laskerian for all $i\leq \dim
M$, then the $R$-module $\Ext^i_R(N,M)$ is weakly Laskerian for all $i\geq 0$
and for any finitely generated $R$-module $N$ with $\Supp_R(N) \subseteq V
(\fa)$ and $\dim N \leq 1$.

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The categories of this paper are: acc-phys
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
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex