Higher residues and canonical pairing on the twisted de Rham cohomology

Abstract

We describe an explicit formula of the canonical pairing on the twisted de Rham cohomology associated with the category of local matrix factorizations and by characterizing its relation to Saito’s higher residue pairings we reprove the conjecture of Shklyarov [Adv. Math. 292 (2016), pp. 181–209].