Opened Access On determinant functors and K-theory

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Autor: Muro Jiménez, Fernando
Tonks, Andrew
Witte, Malte
Departamento: Universidad de Sevilla. Departamento de álgebra
Fecha: 2015
Publicado en: Publicacions matemàtiques, 59 (1), 137-233.
Tipo de documento: Artículo
Resumen: 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.
Cita: Muro Jiménez, F., Tonks, A. y Witte, M. (2015). On determinant functors and K-theory. Publicacions matemàtiques, 59 (1), 137-233.
Tamaño: 799.5Kb
Formato: PDF

URI: http://hdl.handle.net/11441/41875

DOI: http://dx.doi.org/10.5565/PUBLMAT 59115 07

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