2014/03/07 by Carlos E. Parra, Parra, Carlos E., Manuel Saorín +1
Mathematics · #16B50 #16Exx #18Gxx #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16B50 #msc:16Exx #msc:18Gxx
paper · pdf · doi:10.48550/arxiv.1403.1728
New version which incorporates the suggestions of the referees
arxiv created 2015/01/15 · arxiv updated 2015/01/16
Given a torsion pair t = (T ;F) in a module category R-Mod we give necessary and sufficient conditions for the associated Happel-Reiten-Smalø t-structure in D(R) to have a heart Ht which is a module category. We also study when such a pair is given by a 2-term complex of projective modules in the way described by Hoshino-Kato-Miyachi ([HKM]). Among other consequences, we completely identify the hereditary torsion pairs t for which Ht is a module category in the following cases: i) when t is the left constituent of a TTF triple, showing that t need not be HKM; ii) when t is faithful; iii) when t is arbitrary and the ring R is either commutative, semi-hereditary, local, perfect or Artinian. We also give a systematic way of constructing non-tilting torsion pairs for which the heart is a module category generated by a stalk complex at zero