Shklyarov's normalization conjecture for the higher residue pairing

Let QQ be the polynomial ring and ff a polynomial as in the source, let nn be the relevant degree, and let cfCc_f\in\mathbb{C} be the constant such that the canonical pairing on HNn(mf(Q,f))HN_n(mf(Q,f)) corresponds under the Hochschild–Kostant–Rosenberg isomorphism IfI_f to cfunc_f u^n times the higher residue pairing KfK_f on Hf(0)H_f^{(0)}. Shklyarov's conjecture. For any ff,

cf=(1)n(n+1)/2.c_f = (-1)^{n(n+1)/2}.

The prediction specifies the universal normalization constant relating the canonical pairing and the higher residue pairing under the HKR isomorphism. The supplied text gives no resolution status for this prediction.

Sources & referencesView supporting material

Primary source

Michael K. Brown and Mark E. Walker, “A proof of a conjecture of Shklyarov”, arXiv:1909.04088 (2020).

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