Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extensions of a Dualizing Complex by its Ring: Commutative Versions of a
  Conjecture of Tachikawa   Let $(R,\fm,k)$ be a commutative noetherian local ring with dualizing complex
$\dua R$, normalized by $\Ext^{\depth(R)}_R(k,\dua R)\cong k$. Partly motivated
by a long standing conjecture of Tachikawa on (not necessarily commutative)
$k$-algebras of finite rank, we conjecture that if $\Ext^n_R(\dua R,R)=0$ for
all $n>0$, then $R$ is Gorenstein, and prove this in several significant cases.

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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph