Algebraic K-theory of the first Morava K-theory

TL;DR

This paper computes the algebraic K-theory of the first Morava K-theory spectrum modulo p and v_1 using topological cyclic homology, providing insights into its algebraic structure.

Contribution

It introduces a computation of algebraic K-theory for the first Morava K-theory spectrum using topological cyclic homology, a novel approach in this context.

Findings

Computed algebraic K-theory modulo p and v_1 for ell/p

Applied topological cyclic homology to this computation

Enhanced understanding of the algebraic structure of Morava K-theory

Abstract

We compute the algebraic K-theory modulo p and v_1 of the S-algebra ell/p = k(1), using topological cyclic homology.