Given a compact Lie group G and a commutative orthogonal ring spectrum R such that R[G]* = ?*(R ? G+) is finitely generated and projective over ?*(R), we construct a multiplicative G-Tate spectral sequence for each R-module X in orthogonal G-spectra, with E2-page given by the Hopf algebra Tate cohomology of R[G]* with coefficients in ?*(X). Under mild hypotheses, such as X being bounded below and the derived page RE? vanishing, this spectral sequence converges strongly to the homotopy ?*(XtG) of the G-Tate construction XtG = [EG ? F(EG+, X]G.
Reihe
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Verlagsort
Zielgruppe
Maße
Höhe: 254 mm
Breite: 178 mm
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ISBN-13
978-1-4704-6878-1 (9781470468781)
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Schweitzer Klassifikation
Alice Hedenlund, University of Oslo, Norway.
John Rognes, University of Oslo, Norway.
1. Introduction
2. Tate Cohomology for Hopf Algebras
3. Homotopy Groups of Orthogonal $G$-Spectra
4. Sequences of Spectra and Spectral Sequences
5. The $G$-Homotopy Fixed Point Spectral Sequence
6. The $G$-Tate Spectral Sequence
