# Standard Conjecture D for matrix factorizations

## TL;DR

This paper proves a non-commutative version of Grothendieck's Standard Conjecture D for matrix factorizations of isolated hypersurface singularities, establishing positivity of the Euler pairing in characteristic zero.

## Contribution

It introduces the first proof of Standard Conjecture D in the non-commutative setting for matrix factorizations, expanding the scope of the conjecture.

## Key findings

- Euler pairing for matrix factorizations is positive semi-definite
- Established non-commutative Standard Conjecture D in characteristic 0
- Advances understanding of non-commutative algebraic geometry

## Abstract

We prove the non-commutative analogue of Grothendieck's Standard Conjecture D for the dg-category of matrix factorizations of an isolated hypersurface singularity in characteristic 0. Along the way, we show the Euler pairing for such dg-categories of matrix factorizations is positive semi-definite.