The Ro (S¹)-graded equivariant homotopy of THH(Fp)

Abstract

The main result of this thesis is the computation of ... for ... These RO(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 RO(S¹)-graded TR-groups of a ring. In particular, we compute the groups ... for all even dimensional representations a, and the order of these groups for odd dimensional [alpha]. These groups arise in algebraic K-theory computations, and are particularly important to the understanding of the algebraic K-theory of non-regular schemes. We also study RO(S¹)-graded TR-theory as an RO(S¹)-graded Mackey functor. Using Lewis and Mandell's homological algebra tools for graded Mackey functors, we provide examples of how Kunneth spectral sequences can be used to understand RO(S¹)-graded TR.