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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 TRαn(Fp;p) for α R(S1). These R(S1)–graded TR–groups are the equivariant homotopy groups naturally associated to the S1–spectrum THH(Fp), the topological Hochschild S1–spectrum. This computation, which extends a partial result of Hesselholt and Madsen, provides the first example of the R(S1)–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