Standard conjecture D for local stacky matrix factorizations

We establish the non-commutative analogue of Grothendieck’s standard conjecture D for the differential graded category of $G$-equivariant matrix factorizations associated to an isolated hypersurface singularity where $G$ is a finite group.

Keywords

equivariant matrix factorization, standard conjecture D, Milnor fiber, polarized mixed Hodge structure, Chern character, higher residue pairing

2010 Mathematics Subject Classification

Primary 14A22. Secondary 14B05, 32S25, 32S35.

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B. Kim was supported by KIAS individual grant MG016404, and T. Kim was supported by NRF-2018R1D1A3B07043346.

Received 5 July 2023

Received revised 28 September 2023

Accepted 12 October 2023

Published 2 October 2024