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

##### Author(s)

Gerhardt, Teena Meredith
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##### Other Contributors

Massachusetts Institute of Technology. Dept. of Mathematics.

##### Advisor

Lars Hesselholt.

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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.

##### Description

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007. Includes bibliographical references (p. 77-78).

##### Date issued

2007##### Department

Massachusetts Institute of Technology. Dept. of Mathematics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.