On some (co)homological invariants of coherent matrix factorizations

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 $\ell$-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).