26 research outputs found
Recollements of Module Categories
We establish a correspondence between recollements of abelian categories up
to equivalence and certain TTF-triples. For a module category we show,
moreover, a correspondence with idempotent ideals, recovering a theorem of
Jans. Furthermore, we show that a recollement whose terms are module categories
is equivalent to one induced by an idempotent element, thus answering a
question by Kuhn.Comment: Comments are welcom
Criteria for flatness and injectivity
Let be a commutative Noetherian ring. We give criteria for flatness of
-modules in terms of associated primes and torsion-freeness of certain
tensor products. This allows us to develop a criterion for regularity if
has characteristic , or more generally if it has a locally contracting
endomorphism. Dualizing, we give criteria for injectivity of -modules in
terms of coassociated primes and (h-)divisibility of certain \Hom-modules.
Along the way, we develop tools to achieve such a dual result. These include a
careful analysis of the notions of divisibility and h-divisibility (including a
localization result), a theorem on coassociated primes across a \Hom-module
base change, and a local criterion for injectivity.Comment: 19 page
Discrete derived categories I: homomorphisms, autoequivalences and t-structures
Discrete derived categories were studied initially by Vossieck (J Algebra 243:168–176, 2001) and later by Bobiński et al. (Cent Eur J Math 2:19–49, 2004). In this article, we describe the homomorphism hammocks and autoequivalences on these categories. We classify silting objects and bounded t-structures