RO(S^1)-graded TR-groups of F_p, Z and \ell

TL;DR

This paper presents an algorithm for computing RO(S^1)-graded TR-groups of specific rings, completing previous calculations and extending to new cases with applications in algebraic K-theory.

Contribution

It introduces a new algorithm for calculating RO(S^1)-graded TR-groups and provides explicit computations for F_p, Z, and the Adams summand ll.

Findings

Calculated RO(S^1)-graded TR-groups of F_p, Z, and ll.

Extended previous work by completing the calculation for F_p.

Applied results to compute algebraic K-theory of Z-algebras.

Abstract

We give an algorithm for calculating the RO(S^1)-graded TR-groups of F_p, completing the calculation started by the second author. We also calculate the RO(S^1)-graded TR-groups of Z with mod p coefficients and of the Adams summand \ell of connective complex K-theory with V(1)-coefficients. Some of these calculations are used elsewhere to compute the algebraic K-theory of certain Z-algebras.