Article
On determinant functors and K-theory
Author/s | Muro Jiménez, Fernando
Tonks, Andrew Witte, Malte |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2015 |
Deposit Date | 2016-06-06 |
Published in |
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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 ... 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. |
Project ID. | info:eu-repo/grantAgreement/MINECO/MTM2010-15831
info:eu-repo/grantAgreement/MINECO/MTM2013- 42178-P SGR-119-2009 FQM-5713 |
Citation | 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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