# Algebraic $K$-theory of the first Morava $K$-theory

### John Rognes

University of Oslo, Norway### Christian Ausoni

Universität Münster, Germany

## Abstract

For a prime $p \ge 5$, we compute the algebraic $K$-theory modulo $p$ and $v_1$ of the mod $p$ Adams summand, using topological cyclic homology. On the way, we evaluate its modulo $p$ and $v_1$ topological Hochschild homology. Using a localization sequence, we also compute the $K$-theory modulo $p$ and $v_1$ of the first Morava $K$-theory.

## Cite this article

John Rognes, Christian Ausoni, Algebraic $K$-theory of the first Morava $K$-theory. J. Eur. Math. Soc. 14 (2012), no. 4, pp. 1041–1079

DOI 10.4171/JEMS/326