David Rydh: Compact generation of unbounded derived categories of stacks
David Rydh, KTH
Tid: On 2013-10-23 kl 13.15 - 14.15
Plats: Room 3733, Institutionen för matematik, KTH
Ämnesområde: Algebra and Geometry Seminar
I will present recent joint work with Jack Hall and Amnon Neeman on the compact generation of derived categories of stacks. In a loose sense, compact objects in the derived category is a replacement for ample line bundles on projective schemes. The importance of compact objects became clear after the groundbreaking work by Thomason and Neeman in the 90s, not least in relation with duality theory. I'll give a brief introduction to the unbounded derived category and explain why compact objects are of interest.
Our first main result is that compact generation holds for many derived categories of stacks, generalizing earlier results by Thomason, Neeman, Bondal-van der Bergh, Toën and Lurie. Our second main result concerns classifying stacks of groups and some surprising results, both positive and negative, in positive characteristic and for non-affine groups. The latter builds on recent work of Brion.
Our first main result is that compact generation holds for many derived categories of stacks, generalizing earlier results by Thomason, Neeman, Bondal-van der Bergh, Toën and Lurie. Our second main result concerns classifying stacks of groups and some surprising results, both positive and negative, in positive characteristic and for non-affine groups. The latter builds on recent work of Brion.