Generators and dimensions of derived categories

Abstract

Several years ago, Bondal, Rouquier and Van den Bergh introduced the notion of the dimension of a triangulated category, and Rouquier proved that the bounded derived category of coherent sheaves on a separated scheme of finite type over a perfect field has finite dimension. In this paper, we study the dimension of the bounded derived category of finitely generated modules over a commutative Noetherian ring. The main result of this paper asserts that it is finite over a complete local ring containing a field with perfect residue field. Our methods also give a ring-theoretic proof of the affine case of Rouquier's theorem.

27 pages, minor changes, comments welcome

Cited by in corpus (7)

• The radius of a subcategory of modules
• The dimension of a subcategory of modules
• Annihilation of cohomology and strong generation of module categories
• Ulrich ideals and almost Gorenstein rings
• Annihilation of cohomology, generation of modules and finiteness of derived dimension
• Upper bounds for dimensions of singularity categories
• Dimensions of triangulated categories with respect to subcategories