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

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2007

Author dc:creator

• Gerhardt, Teena Meredith

Advisor dc:contributor.advisor

• Lars Hesselholt.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/38934

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/38934