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Abstract
The ``fundamental theorem'' for algebraic Ktheory expresses the Kgroups of a Laurent polynomial ring L[t,t−1] as a direct sum of two copies of the Kgroups of L (with a degree shift in one copy), and certain groups NK±q. It is shown here that a modified version of this result generalises to strongly Zgraded rings; rather than the algebraic Kgroups of L, the splitting involves groups related to the shift actions on the category of Lmodules coming from the graded structure. (These actions are trivial in the classical case). The analogues of the groups NK±q are identified with the reduced Ktheory of homotopy nilpotent twisted endomorphisms, and appropriate versions of MayerVietoris and localisation sequences are established.
Original language  English 

Pages (fromto)  15571599 
Number of pages  43 
Journal  Documenta Mathematica 
Volume  26 
DOIs  
Publication status  Published  01 Nov 2021 
Keywords
 algebraic Ktheory
 strongly Zgraded ring
 fundamental theorem
 BassHellerSwan formula
 projective line
 nil term
 twisted endomorphism
ASJC Scopus subject areas
 Algebra and Number Theory
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Dive into the research topics of 'The "fundamental theorem" for the algebraic Ktheory of strongly Zgraded rings'. Together they form a unique fingerprint.Activities
 1 Invited talk

Fun with Ktheory
Thomas Huettemann (Speaker)
13 May 2022Activity: Talk or presentation types › Invited talk