Matrix factorizations over elementary divisor domains
Dmitry Doryn, Calin Iuliu Lazaroiu, Mehdi Tavakol

TL;DR
This paper investigates the structure of the homotopy category of matrix factorizations over elementary divisor domains, revealing a decomposition into categories of singularities and providing explicit descriptions, even for non-Noetherian rings.
Contribution
It establishes a decomposition of the homotopy category into singularity categories for certain elementary divisor domains, extending results to non-Noetherian cases and explicitly describing these categories.
Findings
Decomposition of homotopy categories into singularity categories
Explicit descriptions of triangulated categories of singularities
Additive generation of cocycle categories by elementary factorizations
Abstract
We study the homotopy category of matrix factorizations of non-zero elements , where is an elementary divisor domain. When has prime elements and factors into a square-free element and a finite product of primes of multiplicity greater than one and which do not divide , we show that is triangle-equivalent with an orthogonal sum of the triangulated categories of singularities of the local Artinian rings , where runs over the prime divisors of of order . This result holds even when is not Noetherian. The triangulated categories are Krull-Schmidt and we describe them explicitly. We also study the cocycle category , showing that it is additively generated by elementary matrix…
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra
