The subject of this monograph lies on the border of algebraic geometry with modern homological algebra. A scheme (in the sense of Grothendieck) is a basic notion in contemporary algebraic geometry, while other basic notions involved (cotorsion modules, and more generally complete cotorsion pairs) are fundamental to homological ring and module theory of the last quarter century. Contraherent cosheaves have been previously introduced by the author and are further presented and developed in this book.
