Muro, Fernando and Tonks, Andrew and Witte, Malte
On determinant functors and K-theory.
Preprintreihe der Fakultät Mathematik 12/2010,
In this paper we introduce a new approach to determinant functors
which allows us to extend Deligne's determinant functors for exact categories
to Waldhausen categories, (strongly) triangulated categories, and derivators.
We construct universal determinant functors in all cases by original methods
which are interesting even for the known cases. Moreover, we show that the
target of each universal determinant functor computes the corresponding K-
theory in dimensions 0 and 1. As applications, we answer open questions by
Maltsiniotis and Neeman on the K-theory of (strongly) triangulated categories
and a question of Grothendieck to Knudsen on determinant functors. We also
prove additivity and localization theorems for low-dimensional K-theory and
obtain generators and (some) relations for various K1-groups.
|Item Type:||Monograph (Working Paper)|
|Institutions:|| Mathematics > Prof. Dr. Harald Garcke|
|Keywords:||determinant functor, K-theory, exact category, Waldhausen category,
triangulated category, Grothendieck derivator|
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||No, this version has not been refereed yet (as with preprints)|
|Created at the University of Regensburg:||Yes|
|Deposited On:||19 Jul 2010 08:47|
|Last Modified:||06 Sep 2011 08:17|