A proof of a conjecture of Shklyarov.

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 (Corollary 2 of [Adv. Math. 292 (2016), 181--209]) and Polishchuk--Vaintrob's Hirzebruch--Riemann--Roch formula for matrix factorizations (Theorem 4.1.4 (i) of [Duke Math. J. 161 (2012), 1863--1926]). [ABSTRACT FROM AUTHOR]