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- W2896794317 abstract "A Laurent polynomial ring $A[t,1/t]$ with coefficients in a unital ring $A$ determines a category of quasi-coherent sheaves on the projective line over $A$; its $K$-theory is known to split into a direct sum of two copies of the $K$-theory of $A$. In this paper, the result is generalised to the case of an arbitrary strongly $mathbb{Z}$-graded ring $R$ in place of the Laurent polynomial ring. The projective line associated with $R$ is indirectly defined by specifying the corresponding category of quasi-coherent sheaves. Notions from algebraic geometry like sheaf cohomology and twisting sheaves are transferred to the new setting, and the $K$-theoretical splitting is established." @default.
- W2896794317 created "2018-10-26" @default.
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- W2896794317 date "2018-10-15" @default.
- W2896794317 modified "2023-09-27" @default.
- W2896794317 title "The algebraic $K$-theory of the projective line associated with a strongly $mathbb{Z}$-graded ring" @default.
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