Matrix factorizations for self-orthogonal categories of modules

2019/05/31 by Bergh, Petter Andreas, Thompson, Peder
#Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1905.13579

Abstract

For a commutative ring S and self-orthogonal subcategory C of Mod(S), we consider matrix factorizations whose modules belong to C. Let f∈ S be a regular element. If f is M-regular for every M∈ C, we show there is a natural embedding of the homotopy category of C-factorizations of f into a corresponding homotopy category of totally acyclic complexes. Moreover, we prove this is an equivalence if C is the category of projective or flat-cotorsion S-modules. Dually, using divisibility in place of regularity, we observe there is a parallel equivalence when C is the category of injective S-modules.

Related

• Complete intersections and equivalences with categories of matrix factorizations
• Matrix factorizations with more than two factors
• The monomorphism category of Gorenstein projective modules and comparision with the category of matrix factorization
• Module factorizations
• Categorical matrix factorizations and monomorphism categories