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

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

2009-02-13

arxiv.org/abs/0902.2334v3

Mathematics

Algebraic Topology

Revised and expanded version, 42 pages.

Scientific paper

10.1007/s00222-010-0239-x

Let p>3 be a prime, let ku be the connective complex K-theory spectrum, and let K(ku) be the algebraic K-theory spectrum of ku. We study the p-primary homotopy type of the spectrum K(ku) by computing its mod (p,v_1) homotopy groups. We show that up to a finite summand, these groups form a finitely generated free module over a polynomial algebra F_p[b], where b is a class of degree 2p+2 defined as a higher Bott element.

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