Chern character for matrix factorizations via Chern-Weil

TL;DR

This paper develops an algebraic Chern-Weil construction for the Chern character of matrix factorizations, generalizing previous results and providing explicit realizations within the framework of smooth algebras.

Contribution

It introduces a new algebraic approach to define the Chern character for matrix factorizations using the Atiyah class, extending existing results to broader algebraic settings.

Findings

Explicit algebraic Chern-Weil type construction for matrix factorizations

Generalization to any smooth $k$-algebra and element $f$

Analysis of basic properties of the Chern character

Abstract

Given a matrix factorization, we use the Atiyah class to give an algebraic Chern-Weil type construction to its Chern character; this allows us to realize the Chern character in an explicit way. It also generalizes the existing result to any smooth $k$-algebra $Q$ ($k$ a commutative ring containing $\mathbb{Q}$) and any $f\in Q$, which agrees with a recent result of Platt. We also study some basic properties of the Chern character.