# Conferenza: Locally coherent hearts t-structures

## Venerdì 27 Marzo 2015, ore 10:30 - Aula 1BC45 - Manolo Saorin

ARGOMENTI: Seminari

Venerdì 27 Marzo 2015, alle ore 10:30 in aula 1BC45, Manolo Saorin (University of Murcia - Spain) terrà una conferenza dal titolo "Locally coherent hearts t-structures".

Abstract
We address the problem of when a t-structure in an triangulated category with coproducts has a heart which is a locally coherent Grothendieck category. We will give sufficient conditions for it to happen when the ambient triangulated category is the derived category of a locally coherent Grothendieck category $\mathcal{G}$, such that $\mathcal{G}$ has a set of generators which are compact objects of $\mathcal{D}(\mathcal{G})$. As an application, we will show:
1) If $\mathbf{t}=(\mathcal{T},\mathcal{F})$ is a finite-type torsion pair in a locally coherent Grothendieck category as indicated above (e.g. the module category over a coherent ring), then the heart of the associated Happel-Reiten-Smalo t-structure is also locally coherent;
2) If $\tau$ is a compactly generated t-structure in the derived category of a Noetherian commutative ring $R$ such that $\tau$ restricts to $\mathcal{D}^b(R)$, then the heart of $\tau$ is a locally coherent Grothendieck category.