The triangular spectrum of matrix factorizations is the singular locus
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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.References
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Additional Information
- Xuan Yu
- Affiliation: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588
- MR Author ID: 1092151
- Email: xuanyumath@gmail.com
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3283-3290
- MSC (2010): Primary 18E30; Secondary 13D02
- DOI: https://doi.org/10.1090/proc/13001
- MathSciNet review: 3503696