Profinite and Continuous Higher K-Theory of Exact Categories, Orders, and Group Rings期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Profinite and Continuous Higher K-Theory of Exact Categories, Orders, and Group Rings

Authors:	Aderemi Kuku

Affiliation:	(1) The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

Abstract:	Let be a rational prime, an exact category. In this article, we define and study for all , the profinite higher K-theory of , that is $K_n^{pr} ({mathcal{C}},hat {mathbb{Z}}_ell ): = [M_{ell ^infty }^{n + 1} ,BQ(mathcal{C})]$ as well as $K_n ({mathcal{C}},hat {mathbb{Z}}_ell ): = lim xleftarrow[S]{}[M_{ell ^infty }^{n + 1} ,BQ({mathcal{C}})]$ , where $M_{ell ^infty }^{n + 1} : = lim xleftarrow[S]{}M_{ell ^S }^{n + 1} {text{ and }}M_{ell ^S }^{n + 1}$ is the -dimensional mod- Moore space. We study connections between $K_n^{pr} ({mathcal{C}},hat {mathbb{Z}}_ell ) and K_n ({mathcal{C}},hat {mathbb{Z}}_ell )$ and prove several -completeness results involving these and associated groups including the cases where is the category of finitely generated (resp. finitely generated projective) modules over orders in semi-simple algebras over number fields and p-adic fields. We also define and study continuous K-theory of orders in p-adic semi-simple algebras and show some connection between the profinite and continuous K-theory of .

Keywords:	higher K-theory exact categories orders group rings Mod-m Moore space profinite continuous semi-simple algebras I-complete
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