#### Volume 8, issue 4 (2008)

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The $R(S^1)$–graded equivariant homotopy of THH($\mathbb{F}_p$)

### Teena Meredith Gerhardt

Algebraic & Geometric Topology 8 (2008) 1961–1987
##### Abstract

The main result of this paper is the computation of TR${}_{\alpha }^{n}\left({\mathbb{F}}_{p};p\right)$ for $\alpha \in R\left({S}^{1}\right)$. These $R\left({S}^{1}\right)$–graded TR–groups are the equivariant homotopy groups naturally associated to the ${S}^{1}$–spectrum THH$\left({\mathbb{F}}_{p}\right)$, the topological Hochschild ${S}^{1}$–spectrum. This computation, which extends a partial result of Hesselholt and Madsen, provides the first example of the $R\left({S}^{1}\right)$–graded TR–groups of a ring. These groups arise in algebraic $K$–theory computations and are particularly important to the understanding of the algebraic $K$–theory of non-regular schemes.