Article ID Journal Published Year Pages File Type
4665100 Advances in Mathematics 2016 55 Pages PDF
Abstract

Building upon ideas of Eisenbud, Buchweitz, Positselski, and others, we introduce the notion of a factorization category. We then develop some essential tools for working with factorization categories, including constructions of resolutions of factorizations from resolutions of their components and derived functors. Using these resolutions, we lift fully-faithfulness and equivalence statements from derived categories of Abelian categories to derived categories of factorizations. Some immediate geometric consequences include a realization of the derived category of a projective hypersurface as matrix factorizations over a noncommutative algebra and recover of a theorem of Baranovsky and Pecharich.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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