“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
Paper IPM / M / 15528  


Abstract:  
Let ModS denote the category of Smodules, where Sis a small preadditive category. Using the notion of relative derived categories of functor categories, we generalize Rickardâs theorem on derived equivalences of module categories over rings to ModS. Several interesting applications will be provided. In particular, it will be shown that derived equivalence of two coherent rings not only implies the equivalence of their homotopy categories of projective modules, but also implies that they are Gorenstein derived equivalent. As another application, it is shown that a good tilting module produces an equivalence between the unbounded derived category of the module category of the ring and the relative derived category of the module category of the endomorphism ring of it.
Download TeX format 

back to top 