Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: When the Schur functor induces a triangle-equivalence between Gorenstein
  defect categories   Let $R$ be an Artin algebra and $e$ an idempotent of $R$. Assume that ${\rm
Tor}_i^{eRe}(Re,G)=0$ for any $G\in{\rm GProj} eRe$ and $i$ sufficiently large.
Necessary and sufficient conditions are given for the Schur functor $S_e$ to
induce a triangle-equivalence $\mathbb{D}_{def}(R)\simeq\mathbb{D}_{def}(eRe)$.
Combine this with a result of Psaroudakis-Skartsaterhagen-Solberg [29], we
provide necessary and sufficient conditions for the singular equivalence
$\mathbb{D}_{sg}(R)\simeq\mathbb{D}_{sg}(eRe)$ to restrict to a
triangle-equivalence $\underline{{\rm GProj} R}\simeq\underline{{\rm GProj}
eRe}$. Applying these to the triangular matrix algebra $T=\left(
  \begin{array}{cc}
  A & M \quad
  0 & B
  \end{array}
  \right)$, corresponding results between candidate categories of $T$ and $A$
(resp. $B$) are obtained. As a consequence, we infer Gorensteinness and
CM-freeness of $T$ from those of $A$ (resp. $B$). Some concrete examples are
given to indicate one can realise the Gorenstein defect category of a
triangular matrix algebra as the singularity category of one of its corner
algabras.

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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an