Corpus ID: 220969001

# Derived categories of skew quadric hypersurfaces

@article{Ueyama2020DerivedCO,
title={Derived categories of skew quadric hypersurfaces},
author={Kenta Ueyama},
journal={arXiv: Rings and Algebras},
year={2020}
}
• Kenta Ueyama
• Published 5 August 2020
• Mathematics
• arXiv: Rings and Algebras
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 $\operatorname{\mathsf{qgr… Expand 1 Citations #### Tables from this paper Noncommutative conics in Calabi-Yau quantum projective planes • Mathematics • 2021 In noncommutative algebraic geometry, noncommutative quadric hyerpersurfaces are major objects of study. In this paper, we give a complete classification of the homogeneous coordinate algebras A ofExpand #### References SHOWING 1-10 OF 45 REFERENCES On Knörrer Periodicity for Quadric Hypersurfaces in Skew Projective Spaces Abstract We study the structure of the stable category$\text{}\underline{\mathsf{CM}}^{\mathbb{Z}}(S/(f))$of graded maximal Cohen–Macaulay module over$S/(f)$where$S$is a graded ($\pm 1$)-skewExpand A categorical characterization of quantum projective spaces • Mathematics • Journal of Noncommutative Geometry • 2021 Let$R$be a finite dimensional algebra of finite global dimension over a field$k$. In this paper, we will characterize a$k$-linear abelian category$\mathscr C$such that$\mathscr C\congExpand
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