Standard conjecture D for local stacky matrix factorizations

TL;DR

This paper proves a non-commutative version of Grothendieck's standard conjecture D for a specific category of matrix factorizations linked to isolated hypersurface singularities with group actions.

Contribution

It establishes the non-commutative analogue of the standard conjecture D for G-equivariant matrix factorizations in the context of isolated hypersurface singularities.

Findings

Proves the non-commutative standard conjecture D for G-equivariant matrix factorizations.

Extends classical conjecture to a non-commutative setting involving hypersurface singularities.

Provides new insights into the structure of differential graded categories in algebraic geometry.

Abstract

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.