A proof of a conjecture of Shklyarov

TL;DR

This paper proves a conjecture linking higher residue pairings with pairings on cyclic homology in matrix factorization categories, providing new proofs of related results and formulas.

Contribution

It establishes the conjecture of Shklyarov and offers new proofs of existing key results in the theory of matrix factorizations.

Findings

Confirmed the conjecture relating pairings in matrix factorizations

Provided new proofs of Shklyarov's results

Re-derived the Hirzebruch-Riemann-Roch formula for matrix factorizations

Abstract

We prove a conjecture of Shklyarov concerning the relationship between K. Saito's higher residue pairing and a certain pairing on the periodic cyclic homology of matrix factorization categories. Along the way, we give new proofs of a result of Shklyarov and Polishchuk-Vaintrob's Hirzebruch-Riemann-Roch formula for matrix factorizations.