5 papers
The homotopy category of pure injective flats and Grothendieck duality
Esmaeil Hosseini
Let (X;OX) be a locally noetherian scheme with a dualizing complex D. We prove that DOX - : K(PinfX)----> K(InjX) is an equivalence of triangulated categories where K(InjX) is the…
Purity and flatness in symmetric monoidal closed exact categories
Esmaeil Hosseini, Ali Zaghian
Let A be a symmetric monoidal closed exact category. This category is a natural framework to define the notions of purity and flatness. We show that an object F in A is flat if and…
The homotopy category of flat functors
Esmaeil Hosseini, Ali Zaghian
Let C be a small category and G be a tensor Grothendieck category. We define a notion of atness in the category Fun(C; G) of all covariant functors from C to G and show that the in…
The Pure derived category of quasi-coherent sheaves
Esmaeil Hosseini
Let X be a quasi-compact and quasi-separated (not necessarily semiseparated) scheme. The category QcoX of all quasi-coherent sheaves of OX-modules has several diferent pure derived…
Flat quasi-coherent sheaves of finite cotorsion dimension
Esmaeil Hosseini
Let X be e quasi-compact and semi-separated scheme. If every at quasi- coherent sheaf has finite cotorsion dimension, we prove that X is n-perfect for some n > 0. If X is coherent…