Homology, Homotopy and Applications

Matrix factorizations over projective schemes

Jesse Burke and Mark E. Walker

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Abstract

We study matrix factorizations of regular global sections of line bundles on schemes. If the line bundle is very ample relative to a Noetherian affine scheme we show that morphisms in the homotopy category of matrix factorizations may be computed as the hypercohomology of a certain mapping complex. Using this explicit description, we prove an analogue of Orlov’s theorem that there is a fully faithful embedding of the homotopy category of matrix factorizations into the singularity category of the corresponding zero subscheme. Moreover, we give a complete description of the image of this functor.

Article information

Source
Homology Homotopy Appl. Volume 14, Number 2 (2012), 37-61.

Dates
First available in Project Euclid: 12 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.hha/1355321479

Mathematical Reviews number (MathSciNet)
MR3007084

Zentralblatt MATH identifier
1259.14015

Subjects
Primary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 13D09: Derived categories 13D02: Syzygies, resolutions, complexes

Keywords
Matrix factorization singularity category

Citation

Burke, Jesse; Walker, Mark E. Matrix factorizations over projective schemes. Homology Homotopy Appl. 14 (2012), no. 2, 37--61.https://projecteuclid.org/euclid.hha/1355321479


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