Title: Picard categories, determinant functors and K-theory
Abstract: I will exhibit connections between:
1) The Knudsen-Mumford theorem on the existence of a unique determinant functor from bounded complexes to invertible sheaves.
2) Deligne's Picard category of virtual objects of an exact category, which models the 1-truncation of its K-theory spectrum.
3) The Gillet-Waldhausen isomorphism between the K-theories of an exact category and its category of bounded complexes.
If time allows I will also show connections with:
4) Determinant functors on triangulated categories with a "triangulated category of true triangles", as suggested by Grothendieck.
5) Maltsiniotis's conjecture on the agreement between the K-theories of an exact category and its triangulated derivator.