Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular equivalences and Auslander-Reiten conjecture   Auslander-Reiten conjecture, which says that an Artin algebra does not have
any non-projective generator with vanishing self-extensions in all positive
degrees, is shown to be invariant under certain singular equivalences induced
by adjoint pairs, which occur often in matrix algebras, recollements and change
of rings. Accordingly, several reduction methods are established to study this
conjecture.

10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat