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Abstract
A Laurent polynomial ring R=S[t, t−1] with coefficients in a unital ring determines a category of quasicoherent sheaves on the projective line over S; its Ktheory is known to split into a direct sum of two copies of the Ktheory of S. In this paper, the result is generalised to the case of an arbitrary strongly Zgraded ring R in place of the Laurent polynomial ring. The projective line associated with R is indirectly defined by specifying the corresponding category of quasicoherent sheaves. Notions from algebraic geometry like sheaf cohomology and twisting sheaves are transferred to the new setting,and the Ktheoretical splitting is established.
Original language  English 

Article number  106425 
Number of pages  20 
Journal  Journal of Pure and Applied Algebra 
Volume  224 
Issue number  12 
Early online date  14 May 2020 
DOIs  
Publication status  Published  Dec 2020 
Keywords
 algebraic Ktheory
 graded algebra
 strongly graded ring
ASJC Scopus subject areas
 Algebra and Number Theory
 Mathematics(all)
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Fun with Ktheory
Thomas Huettemann (Speaker)
13 May 2022Activity: Talk or presentation types › Invited talk

Ktheory: from linear equations to the fundamental theorem
Thomas Huettemann (Speaker)
19 Feb 2021Activity: Talk or presentation types › Oral presentation