Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derived categories of skew quadric hypersurfaces   The existence of a full strong exceptional sequence in the derived category
of a smooth quadric hypersurface was proved by Kapranov. In this paper, we
present a skew generalization of this result. Namely, we show that if $S$ is a
standard graded $(\pm 1)$-skew polynomial algebra in $n$ variables with $n \geq
3$ and $f = x_1^2+\cdots +x_n^2 \in S$, then the derived category
$\operatorname{\mathsf{D^b}}(\operatorname{\mathsf{qgr}} S/(f))$ of the
noncommutative scheme $\operatorname{\mathsf{qgr}} S/(f)$ has a full strong
exceptional sequence. The length of this sequence is given by $n-2+2^r$ where
$r$ is the nullity of a certain matrix over $\mathbb F_2$. As an application,
by studying the endomorphism algebra of this sequence, we obtain the
classification of $\operatorname{\mathsf{D^b}}(\operatorname{\mathsf{qgr}}
S/(f))$ for $n=3, 4$.

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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: stat