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 (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]).
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