Algebra/Topology seminar

Abstract: Given a diagram of schemes, we can ask if a geometric object over one of them can be built from descent data (usually objects of the same type over the various other schemes in the diagram, together with compatibility isomorphisms). We can for example ask this for vector bundles and principal G-bundles for an algebraic group G, but also for more geometric objects such as elliptic curves. All the above mentioned descent problems can be phrased using the language of moduli stacks. In that context, saying that all descent problems for a given diagram have a unique solution is equivalent to saying that the diagram in question is a colimit diagram (in the 2-category of stacks). In my talk I will outline how to use recent generalizations of the Tannakian formalism to study such questions.