24 research outputs found
Strict polynomial functors and coherent functors
We build an explicit link between coherent functors in the sense of Auslander
and strict polynomial functors in the sense of Friedlander and Suslin.
Applications to functor cohomology are discussed.Comment: published version, 24 pages. Section 2.7 reorganized, and notational
distinction between left and right tensor product reinstalle
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
On quiver Grassmannians and orbit closures for representation-finite algebras
We show that Auslander algebras have a unique tilting and cotilting module which is generated and cogenerated by a projective-injective; its endomorphism ring is called the projective quotient algebra. For any representation- nite algebra, we use the projective quotient algebra to construct desingularizations of quiver Grassmannians, orbit closures in representation varieties, and their desingularizations. This generalizes results of Cerulli Irelli, Feigin and Reineke