A proof of a conjecture of Shklyarov

  • Michael K. Brown

    Auburn University, USA
  • Mark E. Walker

    University of Nebraska-Lincoln, USA
A proof of a conjecture of Shklyarov cover
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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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Michael K. Brown, Mark E. Walker, A proof of a conjecture of Shklyarov. J. Noncommut. Geom. 16 (2022), no. 4, pp. 1479–1523

DOI 10.4171/JNCG/501