A Chern-Weil formula for the Chern character of a perfect curved module

TL;DR

This paper develops a Chern-Weil formula for the Chern character of perfect modules over curved algebras, linking algebraic geometry and homological invariants in characteristic zero.

Contribution

It introduces a new Chern-Weil formula for perfect modules over curved algebras, connecting the Chern character to negative cyclic homology of the second kind.

Findings

Derived a Chern-Weil formula for perfect modules

Linked Chern character to negative cyclic homology

Applicable under smoothness conditions on the algebra

Abstract

Let $k$ be a field of characteristic 0 and $\mathcal{A}$ a curved $k$-algebra. We obtain a Chern-Weil-type formula for the Chern character of a perfect $\mathcal{A}$-module taking values in $HN_0^{II}(\mathcal{A})$, the negative cyclic homology of the second kind associated to $\mathcal{A}$, when $\mathcal{A}$ satisfies a certain smoothness condition.