We introduce the notions of multiplier C*-category and continuous bundle of C*-categories, as the categorical analogues of the corresponding C*-algebraic notions. Every symmetric tensor C*-category with conjugates is a continuous bundle of C*-categories, with base space the spectrum of the C*-algebra associated with the identity object. We classify tensor C*-categories with fibre the dual of a ...

We study certain moduli spaces of stable vector bundles of rank two on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing intermediate cohomology. In one case, all except one component of the moduli space has such vector bundles.

In the paper [MTT] a conceptuel description of compactifications of moduli spaces of stable vector bundles on surfaces has been given, whose boundaries consist of vector bundles on trees of sufaces. In this article a typical basic case for the projective plane is described explicitly including the constrution of a relevant Kirwan blow up.

Given a torsion bundle gerbe on a compact smooth manifold or, more generally, on a compact étale Lie groupoid M , we show that the corresponding category of gerbe modules is equivalent to the category of finitely generated projective modules over an Azumaya algebra on M . This result can be seen as an equivariant Serre-Swan theorem for twisted vector bundles.

In this work we deal with actions of vector groupoid which is a new concept in the literature‎. ‎After we give the definition of the action of a vector groupoid on a vector space‎, ‎we obtain some results related to actions of vector groupoids‎. ‎We also apply some characterizations of the category and groupoid theory to vector groupoids‎. ‎As the second part of the work‎, ‎we define the notion...

In this paper we define twisted equivariantK-theory for actions of Lie groupoids. For a Bredon-compatible Lie groupoid G, this defines a periodic cohomology theory on the category of finite G-CW-complexes with G-stable projective bundles. A classification of these bundles is shown. We also obtain a completion theorem and apply these results to proper actions of groups.

We give a concrete description of the category of G-equivariant vector bundles on certain affine G-varieties (where G is a reductive linear algebraic group) in terms of linear algebra data.