
A Multiplicative Tate Spectral Sequence for Compact Lie Group Actions
American Mathematical Society (Publisher)
Published on 31. May 2024
Book
Paperback/Softback
134 pages
978-1-4704-6878-1 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
118 gr
ISBN-13
978-1-4704-6878-1 (9781470468781)
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Schweitzer Classification
Persons
Alice Hedenlund, University of Oslo, Norway.
John Rognes, University of Oslo, Norway.
John Rognes, University of Oslo, Norway.
Content
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
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