Title 



Chow groups of tensor triangulated categories


Author 


 

Abstract 



We recall P. Balmer's definition of tensor triangular Chow group for a tensor triangulated category K and explore some of its properties. We give a proof that for a suitably nice scheme X it recovers the usual notion of Chow group from algebraic geometry when we put K = Dperf (X) Furthermore, we identify a class of functors for which tensor triangular Chow groups behave functorially and show that (for suitably nice schemes) proper pushforward and fiat pullback of algebraic cycles can be interpreted as being induced by the derived inverse and direct image functors between the bounded derived categories of the involved schemes. We also compute some examples for derived and stable categories from modular representation theory, where we obtain tensor triangular cycle groups with torsion coefficients. This illustrates our point of view that tensor triangular cycles are elements of a certain Grothendieck group, rather than Zlinear combinations of closed subspaces of some topological space. (C) 2015 Elsevier B.V. All rights reserved.  

Language 



English


Source (journal) 



Journal of pure and applied algebra.  Amsterdam 

Publication 



Amsterdam : 2016


ISSN 



00224049


Volume/pages 



220:4(2016), p. 13431381


ISI 



000366070600006


Full text (Publisher's DOI) 


 

Full text (publisher's version  intranet only) 


 
