On some (co)homological invariants of coherent matrix factorizations

TL;DR

This paper establishes an equivalence between categories of coherent matrix factorizations and absolute singularities, and computes their l-adic cohomology, Hochschild, and cyclic homologies, advancing understanding of their invariants.

Contribution

It introduces a new equivalence between dg categories of matrix factorizations and singularities, and computes key cohomological invariants.

Findings

Established an equivalence between dg categories of matrix factorizations and absolute singularities.

Computed l-adic cohomology of the dg category of coherent matrix factorizations.

Calculated Hochschild and periodic cyclic homologies in the affine case.

Abstract

We provide an equivalence between the dg category of coherent matrix factorizations and a certain dg category of absolute singularities. As an application, we compute the l-adic cohomology of the dg category of coherent matrix factorizations, as well as its Hochschild and periodic cyclic homologies (these last two only in the affine case).