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Abstract
The ``fundamental theorem'' for algebraic K-theory expresses the K-groups of a Laurent polynomial ring L[t,t−1] as a direct sum of two copies of the K-groups 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 Z-graded rings; rather than the algebraic K-groups of L, the splitting involves groups related to the shift actions on the category of L-modules 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 K-theory of homotopy nilpotent twisted endomorphisms, and appropriate versions of Mayer-Vietoris and localisation sequences are established.
Original language | English |
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Pages (from-to) | 1557-1599 |
Number of pages | 43 |
Journal | Documenta Mathematica |
Volume | 26 |
DOIs | |
Publication status | Published - 01 Nov 2021 |
Keywords
- algebraic K-theory
- strongly Z-graded ring
- fundamental theorem
- Bass-Heller-Swan 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 K-theory of strongly Z-graded rings'. Together they form a unique fingerprint.Activities
- 1 Invited talk
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Fun with K-theory
Thomas Huettemann (Speaker)
13 May 2022Activity: Talk or presentation types › Invited talk