Smooth and proper noncommutative schemes and gluing of dg categories
The author defines noncommutative schemes to be dg-categories satisfying some additional properties. Properties such that compactness, smoothness, and properness are extended to noncommutative schemes. One big class of examples is provided by certain subcategories of perfect complexes on smooth projective schemes. Furthermore, a gluing operation for noncommutative schemes is defined via bimodules of dg-categories. From these a number of results are shown about finite-dimensional algebras and noncommutative projective planes.
scientific article; zbMATH DE number 6631654
scientific article