On locally coherent hearts

Let G be a locally coherent Grothendieck category.We show that, under particular conditions, if a t-structure τ in the unbounded derived category D(G) restricts to the bounded derived category D b (fp(G)) of its category of finitely presented (i.e, coherent) objects, then its heart H τ is a locally coherent Grothendieck category on which H τ ∩ D b (fp(G)) is the class of finitely presented objects.Those particular conditions are always satisfied when G is arbitrary and τ is the Happel-Reiten-Smalø t-structure in D(G) associated to a torsion pair in fp(G) or when G = Qcoh(‫)ޘ‬ is the category of quasicoherent sheaves on a noetherian affine scheme ‫ޘ‬ and τ is any compactly generated t-structure in D(‫)ޘ‬ := D(Qcoh(‫))ޘ‬ which restricts to D b ‫)ޘ(‬ := D b (coh(‫.))ޘ‬In particular, the heart of any t-structure in D b ‫)ޘ(‬ is the category of finitely presented objects of a locally coherent Grothendieck category.