On hearts which are module categories
Abstract
Given a torsion pair $\mathbf{t} = (\mathcal{T} ;\mathcal{F})$ in a module category $R$Mod we give necessary and sufficient conditions for the associated HappelReitenSmalø$\text{ }$ tstructure in $\mathcal{D}(R)$ to have a heart $\mathcal{H}_{\mathbf{t}}$ which is a module category. We also study when such a pair is given by a 2term complex of projective modules in the way described by HoshinoKatoMiyachi ([HKM]). Among other consequences, we completely identify the hereditary torsion pairs $\mathbf{t}$ for which $\mathcal{H}_{\mathbf{t}}$ is a module category in the following cases: i) when $\mathbf{t}$ is the left constituent of a TTF triple, showing that $\mathbf{t}$ need not be HKM; ii) when $\mathbf{t}$ is faithful; iii) when $\mathbf{t}$ is arbitrary and the ring $R$ is either commutative, semihereditary, local, perfect or Artinian. We also give a systematic way of constructing nontilting torsion pairs for which the heart is a module category generated by a stalk complex at zero
 Publication:

arXiv eprints
 Pub Date:
 March 2014
 arXiv:
 arXiv:1403.1728
 Bibcode:
 2014arXiv1403.1728P
 Keywords:

 Mathematics  Representation Theory;
 16Exx;
 18Gxx;
 16B50
 EPrint:
 New version which incorporates the suggestions of the referees