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The triangular spectrum of matrix factorizations is the singular locus


Author: Xuan Yu
Journal: Proc. Amer. Math. Soc. 144 (2016), 3283-3290
MSC (2010): Primary 18E30; Secondary 13D02
DOI: https://doi.org/10.1090/proc/13001
Published electronically: February 2, 2016
MathSciNet review: 3503696
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Abstract:

The singularity category of a ring/scheme is a triangulated category defined to capture the singularities of the ring/scheme. In the case of a hypersurface $ R/f$, it is given by the homotopy category of matrix factorizations $ [MF(R,f)]$. In this paper, we apply Balmer's theory of tensor triangular geometry to matrix factorizations by taking into consideration their tensor product. We show that the underlying topological space of the triangular spectrum of $ [MF(R,f)]$ is the singular locus of the hypersurface by using a support theory developed by M. Walker.


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Additional Information

Xuan Yu
Affiliation: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588
Email: xuanyumath@gmail.com

DOI: https://doi.org/10.1090/proc/13001
Received by editor(s): November 5, 2014
Received by editor(s) in revised form: October 9, 2015
Published electronically: February 2, 2016
Communicated by: Irena Peeva
Article copyright: © Copyright 2016 American Mathematical Society

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