Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative Singularity Categories   We study the properties of the relative derived category
$D_{\mathscr{C}}^{b}$($\mathscr{A}$) of an abelian category $\mathscr{A}$
relative to a full and additive subcategory $\mathscr{C}$. In particular, when
$\mathscr{A}=A{\text -}\mod$ for a finite-dimensional algebra $A$ over a field
and $\mathscr{C}$ is a contravariantly finite subcategory of $A$-$\mod$ which
is admissible and closed under direct summands, the $\mathscr{C}$-singularity
category $D_{\mathscr{C}{\text
sg}}$($\mathscr{A}$)=$D_{\mathscr{C}}^{b}$($\mathscr{A}$)/$K^{b}(\mathscr{C})$
is studied. We give a sufficient condition when this category is triangulated
equivalent to the stable category of the Gorenstein category
$\mathscr{G}(\mathscr{C})$ of $\mathscr{C}$.

22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
10
The categories of this paper are: q-bio