Resolutions in factorization categories

Matthew Ballard, Dragos Deliu, David Favero, M. Umut Isik, Ludmil Katzarkov

Research output: Contribution to journalArticle

8 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)195-249
Number of pages55
JournalAdvances in Mathematics
Volume295
DOIs
StatePublished - Jun 4 2016

Keywords

  • Derived categories
  • Homological algebra
  • Matrix factorizations

ASJC Scopus subject areas

  • Mathematics(all)

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