The algebraic $K$-theory of the projective line associated with a strongly $\mathbb{Z}$-graded ring

Autor:	Huettemann, Thomas, Montgomery, Tasha
Rok vydání:	2018
Předmět:	Mathematics - K-Theory and Homology Mathematics - Rings and Algebras 19D55 16W50 19E99
Druh dokumentu:	Working Paper
Popis:	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. Comment: 22 pages; v2: 23 pages, minor changes, added paragraph on motivation
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1810.06272 Zobrazit plný text záznamu View this record from Arxiv