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Determinant functors on triangulated categories

Published online by Cambridge University Press:  21 July 2010

Manuel Breuning
Manuel Breuning
Affiliation:
King's College London, Department of Mathematics, Strand, London WC2R 2LS, United Kingdom, manuel.breuning@kcl.ac.uk
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Abstract

We study determinant functors which are defined on a triangulated category and take values in a Picard category. The two main results are the existence of a universal determinant functor for every small triangulated category, and a comparison theorem for determinant functors on a triangulated category with a non-degenerate bounded t-structure and determinant functors on its heart. For a small triangulated category Τ we give a natural definition of groups K0(Τ) and K1(Τ) in terms of the universal determinant functor on Τ, and we show that Ki(Τ) ≅ Ki(ε) for i = 0 and 1 if Τ has a non-degenerate bounded t-structure with heart ε.

Keywords

Determinant functorTriangulated categoryPicard categoryK-theory

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Type
Research Article
Information
Journal of K-Theory , Volume 8 , Issue 2 , October 2011 , pp. 251 - 291
Copyright
Copyright © ISOPP 2010

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