6 papers
Derived, coderived, and contraderived categories of locally presentable abelian categories
Leonid Positselski, Jan Stovicek
For a locally presentable abelian category with a projective generator, we construct the projective derived and contraderived model structures on the category of comple…
Unbounded derived categories of small and big modules: Is the natural functor fully faithful?
Leonid Positselski, Olaf M. Schnürer
Consider the obvious functor from the unbounded derived category of all finitely generated modules over a left noetherian ring to the unbounded derived category of all modules.…
Cofibrant generation of pure monomorphisms
Michael Lieberman, Leonid Positselski, Jiri Rosicky +1
We show that pure monomorphisms are cofibrantly generated---generated from a set of morphisms by pushouts, transfinite composition, and retracts---in any locally finitely presentab…
Matlis category equivalences for a ring epimorphism
Silvana Bazzoni, Leonid Positselski
Under mild assumptions, we construct the two Matlis additive category equivalences for an associative ring epimorphism . Assuming that the ring epimorphism is homol…
Exactness of direct limits for abelian categories with an injective cogenerator
Leonid Positselski, Jan Stovicek
We prove that the exactness of direct limits in an abelian category with products and an injective cogenerator J is equivalent to a condition on J which is well-known to characteri…
Noncommutative Kummer theory
Leonid Positselski
We discuss lifting properties of continuous homomorphisms from absolute Galois groups into (pro)finite groups. An analogy with the Langlands program is pointed out in the beginning…