2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59166Let C be a connected noetherian hereditary abelian Ext-finite category with Serre functor over an algebraically closed field k, with finite dimensional homomorphism and extension spaces. Using the classification of such categories from math.RT/9911242, we prove that if C has some object of infinite length, then the Grothendieck group of C is finitely generated if and only if C has a tilting object.Representation Theory16G30text