937 research outputs found
Classifying subcategories and the spectrum of a locally noetherian category
Let be a locally noetherian Grothendieck category. In this
paper, we study subcategories of using subsets of the spectrum
. Along the way, we also develop results in local
algebra with respect to the category that we believe to be of
independent interest.Comment: 40 pages, some new results adde
Finite homological dimension and a derived equivalence
For a Cohen-Macaulay ring , we exhibit the equivalence of the bounded
derived categories of certain resolving subcategories, which, amongst other
results, yields an equivalence of the bounded derived category of finite length
and finite projective dimension modules with the bounded derived category of
projective modules with finite length homologies. This yields isomorphisms of
various generalized cohomology groups (like K-theory) and improves on terms of
a spectral sequence and Gersten complexes.Comment: 23 pages : Some parts of the article changed, especially section 3,
to add clarity. Other minor corrections mad
Coidempotent subcoalgebras and short exact sequences of finitary 2-representations
In this article, we study short exact sequences of finitary 2-representations of a weakly fiat 2-category. We provide a correspondence between such short exact sequences with fixed middle term and coidempotent subcoalgebras of a coalgebra 1-morphism defining this middle term. We additionally relate these to recollements of the underlying abelian 2-representations
Equivariant differential characters and symplectic reduction
We describe equivariant differential characters (classifying equivariant
circle bundles with connections), their prequantization, and reduction
- …