  We study matrix factorization and curved module categories for
Landau-Ginzburg models (X,W) with X a smooth variety, extending parts of the
work of Dyckerhoff. Following Positselski, we equip these categories with model
category structures. Using results of Rouquier and Orlov, we identify compact
generators. Via To\"en's derived Morita theory, we identify Hochschild
cohomology with derived endomorphisms of the diagonal curved module; we compute
the latter and get the expected result. Finally, we show that our categories
are smooth, proper when the singular locus of W is proper, and Calabi-Yau when
the total space X is Calabi-Yau.
