Homological theory of recollements of abelian categories

We investigate several homological aspects of recollements of abelian categories. In particular, we study how various homological invariants and dimensions of the categories involved in a recollement situation are related, and when recollements of abelian categories induce recollements at the level of the bounded derived categories. Finally we give applications to global, finitistic, and representation dimension of rings and Artin algebras, and to Rouquierʼs dimension of triangulated categories.