Tilting preserves finite global dimension

Abstract

Given a tilting object of the derived category of an abelian category of finite global dimension, we give (under suitable finiteness conditions) a bound for the global dimension of its endomorphism ring.

8 pages. Extended the introduction, including some historical comments. Revised the proof of Theorem 1, fixing an error. Added details about derived (co)limits. Accepted for publication with Comptes Rendus Mathématique