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On determinant functors and K-theory
journal contributionposted on 2019-02-28, 11:55 authored by F Muro, A Tonks, M Witte
We extend Deligne’s notion of determinant functor to Waldhausen categories and (strongly) triangulated categories. We construct explicit universal determinant functors in each case, whose target is an algebraic model for the 1-type of the corresponding K-theory spectrum. 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 theorems for low-dimensional K-theory of (strongly) triangulated categories and obtain generators and (some) relations for various K1-groups. This is achieved via a unified theory of determinant functors which can be applied in further contexts, such as derivators.
The first and second authors were partially supported by the Spanish Ministry of Economy and Competitiveness under the grants MTM2010-15831 and MTM2013-42178-P, and by the Government of Catalonia under the grant SGR-119-2009. The first author was also partially supported by the Spanish Ministry of Science and Innovation under a Ram´on y Cajal research contract and by the Andalusian Ministry of Economy, Innovation and Science under the grant FQM-5713.
CitationPublicacions Matemàtiques, 2015, 59, pp. 137-233
Author affiliation/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics
- AM (Accepted Manuscript)