dc.contributor.author |
Muro, Fernando |
dc.contributor.author |
Tonks, Andrew |
dc.contributor.author |
Witte, Malte |
dc.date |
2015 |
dc.identifier |
https://ddd.uab.cat/record/128226 |
dc.identifier |
urn:10.5565/PUBLMAT_59115_07 |
dc.identifier |
urn:oai:ddd.uab.cat:128226 |
dc.identifier |
urn:articleid:20144350v59n1p137 |
dc.identifier |
urn:oai:raco.cat:article/287250 |
dc.identifier |
urn:scopus_id:84920964455 |
dc.identifier |
urn:wos_id:000351416300007 |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
|
dc.relation |
Publicacions matemàtiques ; Vol. 59 Núm. 1 (2015), p. 137-233 |
dc.rights |
open access |
dc.rights |
Tots els drets reservats. |
dc.rights |
https://rightsstatements.org/vocab/InC/1.0/ |
dc.subject |
Determinant functor |
dc.subject |
K-theory |
dc.subject |
Exact category |
dc.subject |
Waldhausen category |
dc.subject |
Triangulated category |
dc.subject |
Grothendieck derivator |
dc.title |
On determinant functors and K-theory |
dc.type |
Article |
dc.description.abstract |
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. |
dc.description.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 unfied theory of determinant functors which can be applied in further contexts, such as derivators. |