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

摘要

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