Chern Character for Global Matrix Factorizations

Abstract: We give a formula for the Chern character on the DG-category of global matrix factorizations on a smooth scheme $X$ with superpotential $w\in \Gamma(\mathcal{O}_X)$. Our formula takes values in a Cech model for Hochschild homology. Our methods may also be adapted to get an explicit formula for the Chern character for perfect complexes of sheaves on $X$ taking values in right derived global sections of the De-Rham algebra. Along the way we prove that the DG version of the Chern character coincides with the classical one for perfect complexes.