Título:
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On determinant functors and K-theory
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Autor/a:
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Muro, Fernando; Tonks, Andrew; Witte, Malte
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Abstract:
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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. |
Abstract:
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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. |
Materia(s):
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-Determinant functor -K-theory -Exact category -Waldhausen category -Triangulated category -Grothendieck derivator |
Derechos:
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open access
Tots els drets reservats.
https://rightsstatements.org/vocab/InC/1.0/ |
Tipo de documento:
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Article |
Editor:
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Compartir:
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Uri:
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https://ddd.uab.cat/record/128226
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