On the algebraic K-theory of the complex K-theory spectrum

• 成果类型: Article
• 署名作者: Ausoni, Christian
• 署名单位: University of Bonn
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0239-x
• 发表日期: 2010
• 页码: 611-668
• 关键词: topological hochschild homology; STABLE-HOMOTOPY; trace

摘要

Let p >= 5 be a prime, let ku be the connective complex K-theory spectrum, and let K(ku) be the algebraic K-theory spectrum of ku. In this paper we study the p-primary homotopy type of the spectrum K(ku) by computing its mod (p, nu(1)) homotopy groups. We show that up to a finite summand, these groups form a finitely generated free module over the polynomial algebra F-p[b], where b is a class of degree 2p + 2 defined as a higher Bott element.