Additivity for derivator K-theory

Denis Charles Cisinski; Amnon Neeman

doi:10.1016/j.aim.2007.10.003

Additivity for derivator K-theory

Denis Charles Cisinski
, Amnon Neeman^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

Abstract

We prove the additivity theorem for the K-theory of triangulated derivators. This solves one of the conjectures made by Maltsiniotis in [G. Maltsiniotis, La K-théorie d'un dérivateur triangulé, in: Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack, Amnon Neeman (Eds.), Categories in Algebra, Geometry and Physics, Conference and Workshop in honor of Ross Street's 60th Birthday, in: Contemp. Math., vol. 431, Amer. Math. Soc., 2007, pp. 341-368]. We also review some basic definitions and results in the theory of derivators in the sense of Grothendieck.

Original language	English
Pages (from-to)	1381-1475
Number of pages	95
Journal	Advances in Mathematics
Volume	217
Issue number	4
DOIs	https://doi.org/10.1016/j.aim.2007.10.003
Publication status	Published - 1 Mar 2008

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title = "Additivity for derivator K-theory",

abstract = "We prove the additivity theorem for the K-theory of triangulated derivators. This solves one of the conjectures made by Maltsiniotis in [G. Maltsiniotis, La K-th{\'e}orie d'un d{\'e}rivateur triangul{\'e}, in: Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack, Amnon Neeman (Eds.), Categories in Algebra, Geometry and Physics, Conference and Workshop in honor of Ross Street's 60th Birthday, in: Contemp. Math., vol. 431, Amer. Math. Soc., 2007, pp. 341-368]. We also review some basic definitions and results in the theory of derivators in the sense of Grothendieck.",

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N2 - We prove the additivity theorem for the K-theory of triangulated derivators. This solves one of the conjectures made by Maltsiniotis in [G. Maltsiniotis, La K-théorie d'un dérivateur triangulé, in: Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack, Amnon Neeman (Eds.), Categories in Algebra, Geometry and Physics, Conference and Workshop in honor of Ross Street's 60th Birthday, in: Contemp. Math., vol. 431, Amer. Math. Soc., 2007, pp. 341-368]. We also review some basic definitions and results in the theory of derivators in the sense of Grothendieck.

AB - We prove the additivity theorem for the K-theory of triangulated derivators. This solves one of the conjectures made by Maltsiniotis in [G. Maltsiniotis, La K-théorie d'un dérivateur triangulé, in: Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack, Amnon Neeman (Eds.), Categories in Algebra, Geometry and Physics, Conference and Workshop in honor of Ross Street's 60th Birthday, in: Contemp. Math., vol. 431, Amer. Math. Soc., 2007, pp. 341-368]. We also review some basic definitions and results in the theory of derivators in the sense of Grothendieck.

KW - Derivators

KW - K-theory

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DO - 10.1016/j.aim.2007.10.003

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VL - 217

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EP - 1475

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 4

ER -

Additivity for derivator K-theory

Abstract

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