On determinant functors and K-theory
Muro, Fernando (Universidad de Sevilla. Facultad de Matemáticas)
Tonks, Andrew (University of Leicester. Department of Mathematics)
Witte, Malte (Ruprecht-Karls-Universität Heidelberg. Mathematisches Institut)

Data:	2015
Resum:	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 unfied theory of determinant functors which can be applied in further contexts, such as derivators.
Nota:	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. Thefirst author was also partially supported by the Spanish Ministry of Science and Innovation under a Ramón y Cajal research contract and by the Andalusian Ministry of Economy, Innovation and Science under the grant FQM-5713.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Determinant functor ; K-theory ; Exact category ; Waldhausen category ; Triangulated category ; Grothendieck derivator
Publicat a:	Publicacions matemàtiques, Vol. 59 Núm. 1 (2015) , p. 137-233, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/287250
DOI: 10.5565/PUBLMAT_59115_07

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