Complete intersections and equivalences with categories of matrix factorizations

2015/09/14 by Bergh, Petter Andreas, Jorgensen, David A.
#13D02 #13D09 #18E30 #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1509.04204

Abstract

We prove that one can realize certain triangulated subcategories of the singularity category of a complete intersection as homotopy categories of matrix factorizations. Moreover, we prove that for any commutative ring and non-zerodivisor, the homotopy category of matrix factorizations embeds into the homotopy category of totally acyclic complexes of finitely generated projective modules over the factor ring.

Related

• Matrix factorizations in higher codimension
• Matrix factorizations over elementary divisor domains
• Matrix factorizations for self-orthogonal categories of modules
• Homotopy category of N-complexes of projective modules
• Categorical matrix factorizations and monomorphism categories