Witt Vectors and Equivariant Ring Spectra

Details Witt Vectors and Equivariant Ring Spectra Witt Vectors and Equivariant Ring Spectra

2004-11-25

arxiv.org/abs/math/0411567v1

Mathematics

Algebraic Topology

35 pages

Scientific paper

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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