The R(S^1)-graded equivariant homotopy of THH(F_p)

TL;DR

This paper computes the R(S^1)-graded TR-groups of the ring F_p, extending previous partial results and providing the first example of such groups, which are crucial for algebraic K-theory of schemes.

Contribution

It extends prior work by explicitly computing R(S^1)-graded TR-groups for F_p, a first in the field, enhancing understanding of algebraic K-theory.

Findings

Computed TR^n_{α}(F_p;p) for α in R(S^1)

Extended partial results of Hesselholt and Madsen

Provided the first example of R(S^1)-graded TR-groups

Abstract

The main result of this paper is the computation of TR^n_{\alpha}(F_p;p) for \alpha in R(S^1). These R(S^1)-graded TR-groups are the equivariant homotopy groups naturally associated to the S^1-spectrum THH(F_p), the topological Hochschild S^1-spectrum. This computation, which extends a partial result of Hesselholt and Madsen, provides the first example of the R(S^1)-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.