Starting with a Grothendieck category G and a torsion pair t D. T; F/in G, we study the local
finite presentability and local coherence of the heart Ht of the associated Happel–Reiten–
Smalø t-structure in the derived category DG/. We start by showing that, in this general
setting, the torsion pair t is of finite type, if and only if it is quasi-cotilting, if and only if it is
cosilting. We then proceed to study those t for which Ht is locally finitely presented, obtaining
a complete answer under some additional assumptions on the ground category G, which are …