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

Abstract

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.

Revised and expanded version, 42 pages.

References in corpus (3)

• Units of ring spectra and their traces in algebraic K-theory
• The localization sequence for the algebraic K-theory of topological K-theory
• Differentials in the homological homotopy fixed point spectral sequence

Cited by in corpus (8)

• Rational algebraic K-theory of topological K-theory
• A higher chromatic analogue of the image of J
• Some recent advances in topological Hochschild homology
• Twisted iterated algebraic K-theory and topological T-duality for sphere bundles
• Purity in chromatically localized algebraic $K$-theory
• On the Brun spectral sequence for topological Hochschild homology
• The topological Hochschild homology of algebraic $K$-theory of finite fields
• Algebraic K-theory of elliptic cohomology