The strong global dimension of piecewise hereditary algebras

Let A be a finite-dimensional piecewise hereditary algebra over an algebraically closed field. This text investigates the strong global dimension of A. This invariant is characterised in terms of the lengths of sequences of tilting mutations relating A to a hereditary abelian category, in terms of the generating hereditary abelian subcategories of the derived category of A, and in terms of the Auslander-Reiten structure of that derived category.