Title: Algebraic K-theory of topological K-theory
Author: Christian Ausoni
Author2: John Rognes
Email: ausoni@math.ethz.ch
Email2: rognes@math.uio.no
Abstract:
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.