for a noetherian scheme, we introduce its unbounded stable derived category. this leads to a
recollement which reflects the passage from the bounded derived category of coherent …

It is possible to associate a topological space to the category of modules over any ring. This
space, the Ziegler spectrum, is based on the indecomposable pure-injective modules …

Let R be a ring. We prove that the homotopy category K (R-Proj) is always \aleph_1-
compactly generated, and, depending on the ring R, it may or may not be compactly …

It is proved that for a commutative noetherian ring with dualizing complex the homotopy
category of projective modules is equivalent, as a triangulated category, to the homotopy …

Given a locally coherent Grothendieck category G, we prove that the homotopy category of
complexes of injective objects (also known as the coderived category of G) is compactly …

We show that Quillenʼs small object argument works for exact categories under very mild
conditions. This has immediate applications to cotorsion pairs and their relation to the …

We define the triangulated category of relative singularities of a closed subscheme in a
scheme. When the closed subscheme is a Cartier divisor, we consider matrix factorizations …

This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based
on the author's memoir L. Positselski, Memoirs of the American Math. Society 212 (2011) …

Page 1 Instytut Matematyczny PAN New Series Homological Algebra of Semimodules and
Semicontramodules Page 2 tº Birkhäuser Page 3 Instytut Matematyczny Polskiej Akademii Nauk …

Our aim is to give a fairly complete account on the construction of compatible model
structures on exact categories and symmetric monoidal exact categories, in some cases …