Dualizing complexes and tilting complexes over simple rings Academic Article uri icon

abstract

  • Simple rings, like fields, are literally 'simple'in many ways. Hence quite a few invariants of rings become trivial for simple rings. We show that this principle applies to the derived Picard group, which classifies dualizing complexes over a ring. In this paper all rings are algebras over a base field k, ring homomorphisms are all over k, and bimodules are all k- central. The symbol⊗ denotes⊗ k. For a ring B, B◦ denotes the opposite ring. We shall write ModA for the category of left A-modules, and Db (ModA) will stand for the bounded derived category. A brief review of key definitions such as dualizing complexes, two-sided tilting complexes and the derived Picard group DPic (A) is included in the body of the paper.

publication date

  • January 1, 2002