Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unifying two results of D. Orlov   Let $\mathbb{X}$ be a noetherian separated scheme $\mathbb{X}$ of finite
Krull dimension which has enough locally free sheaves of finite rank and let
$U\subseteq \mathbb{X}$ be an open subscheme. We prove that the singularity
category of $U$ is triangle equivalent to the Verdier quotient category of the
singularity category of $\mathbb{X}$ with respect to the thick triangulated
subcategory generated by sheaves supported in the complement of $U$. The result
unifies two results of D. Orlov. We also prove a noncommutative version of this
result.

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The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
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The categories of this paper are: adap-org