Opened Access On determinant functors and K-theory

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Author: Muro Jiménez, Fernando
Tonks, Andrew
Witte, Malte
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2015
Published in: Publicacions matemàtiques, 59 (1), 137-233.
Document type: Article
Abstract: 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.
Cite: Muro Jiménez, F., Tonks, A. y Witte, M. (2015). On determinant functors and K-theory. Publicacions matemàtiques, 59 (1), 137-233.
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DOI: 10.5565/PUBLMAT_59115_07

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