Compact generators in categories of matrix factorizations

Understand

We study the category of matrix factorizations associated to the germ of an isolated hypersurface singularity.

• This category is shown to admit a compact generator which is given by the stabilization of the residue field.
• We deduce a quasi-equivalence between the category of matrix factorizations and the dg derived category of an explicitly computable dg algebra.
• Building on this result, we employ a variant of Toen's derived Morita theory to identify continuous functors between matrix factorization categories as integral transforms.