The Topological Hochschild Homology of Algebraic K-theory of finite Fields

In this talk I will explain how to generalize a spectral sequence of Brun for the computation of topological Hochschild homology. As a first example we use the generalized Brun spectral sequence to give a simple computation of the mod $p$ and $v_1$ topological Hochschild homology of connective complex $K$-theory which has first been calculated by Ausoni using the Bökstedt spectral sequence. We then consider the generalized Brun spectral sequence for the topological Hochschild homology of algebraic $K$-theory of finite fields.