### Algebraic K-theory of topological K-theory, by Christian Ausoni and John Rognes

Let l_p = BP<1>_p be the p-complete connective Adams summand of
topological K-theory, and let V(1) be the Smith-Toda complex. For p>3
we explicitly compute the V(1)-homotopy of the algebraic K-theory spectrum
of l_p. In particular we find that it is a free finitely generated module
over the polynomial algebra P(v_2), except for a sporadic class in degree
2p-3. Thus also in this case algebraic K-theory increases chromatic
complexity by one. The proof uses the cyclotomic trace map from algebraic
K-theory to topological cyclic homology, and the calculation is actually
made in the V(1)-homotopy of the topological cyclic homology of l_p.

Christian Ausoni <ausoni@math.ethz.ch>

John Rognes <rognes@math.uio.no>