A proof of a conjecture of Shklyarov

[摘要] 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]).

[学科分类] 神经科学

[关键词] Hochschild homology;matrix factorizations;residue pairing