Witt Vectors and Equivariant Ring Spectra

2004/11/25 by Morten Brun, Brun, Morten · 3 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:13K05 #msc:55P43 #msc:57R85

paper · pdf · doi:10.48550/arxiv.math/0411567

35 pages

arxiv created 2004/11/25 · arxiv updated 2009/12/01

Abstract

This paper establishes a connection between equivariant ring spectra and Witt vectors in the sense of Dress and Siebeneicher. Given a commutative ringspectrum T in the highly structured sense, that is, an E-infinity-ringspectrum, with action of a finite group G we construct a ringhomomorphism from the ring of G-typical Witt vectors of the zeroth homotopy group of T to the zeroth homotopy group of the G-fixed point spectrum of T. In the particular case, where T is the periodic unitary cobordism spectrum introduced by Strickland, we show that this ringhomomorphism is injective, and we interpret this in terms of equivariant cobordism.

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