The R(S1)–graded equivariant homotopy of THH(𝔽p)

Gerhardt, Teena

doi:10.2140/agt.2008.8.1961

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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

DOI: 10.2140/agt.2008.8.1961

Abstract

The main result of this paper is the computation of TR $_{α}^{n} (F_{p}; p)$ for $α \in R (S^{1})$ . 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.

Keywords

K-theory, TR-theory, R(S^1)-graded homotopy

Mathematical Subject Classification 2000

Primary: 19D50, 19D55, 55P91

References

Publication

Received: 13 November 2007

Revised: 24 July 2008

Accepted: 10 September 2009

Published: 22 October 2008

Authors

Teena Meredith Gerhardt
114 E 6th St Unit A Bloomington IN 47408 USA
http://mypage.iu.edu/~tgerhard/Home.html

Volume 8, issue 4 (2008)