Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Results about Endomorphism Rings for Local Cohomology Defined by a
  Pair of Ideals   Let $(R,\mathfrak{m},k)$ denote a local ring. For $I$ and $J$ ideals of $R$,
for all integer $i$, let $H^i_{I,J}(-)$ denote the $i$-th local cohomology
functor with respect to $(I,J)$. Here we give a generalized version of Local
Duality Theorem for local cohomology defined by a pair of ideals. Also, for $M$
be a finitely generated $R$-module, we study the behavior of the endomorphism
rings $H^t_{I,J}(M)$ and $D(H^t_{I,J}(M))$ where $t$ is the smallest integer
such that the local cohomology with respect to a pair of ideals is non-zero and
$D(-):= {\rm Hom}_R(-,E_R(k))$ is the Matlis dual functor. We show too that if
$R$ be a $d$-dimensional complete Cohen-Macaulay and $H^i_{I,J}(R)=0$ for all
$i\neq t$, the natural homomorphism $R\rightarrow {\rm Hom}_R(H^t_{I,J}(K_R),
H^t_{I,J}(K_R))$ is an isomorphism and for all $i\neq t$, where $K_R$ denote
the canonical module of $R$.

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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph