I will explain a proposal (proven under certain assumptions) how to think about the relative K-group K_0(order, R) in an alternative way. Following Burns-Flach, this is the group where the [noncommutative] equivariant Tamagawa number lives. The rough idea to look at it differently: The universal determinant functor of the category of LCA-groups (locally compact abelian) turns out to be, suitably formulated, the classical Haar measure. So, to get an "equivariant measure" (whatever these words a priori might mean...), one could look at the universal determinant functor of LCA-groups, equipped with an action of the order. It turns out, e.g. if the order is hereditary, that the absolute K1-group of this category agrees with the relative K-group in the Burns-Flach formulation. A technical issue which might have discouraged people from looking at the category of LCA groups is that, because of the topology on its objects, it is not abelian. However, it is an exact category, and thus can be handled pretty much like the category of projective modules. There is an explicit generator-relator presentation for K1 of any exact category, which is very different from the Swan presentation [P, phi, Q] of the relative K-group formulation, and we will discuss the explicit comparison problem a little.
Freitag, den 23. November 2018 um 13:30 Uhr, in INF 205, SR A Freitag, den 23. November 2018 at 13:30, in INF 205, SR A
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Otmar Venjakob