A multiplicative tate spectral sequence for compact Lie group actions
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Bibliographic Information
A multiplicative tate spectral sequence for compact Lie group actions
（Memoirs of the American Mathematical Society, no. 1468）
American Mathematical Society, c2024
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"February 2024, volume 294, number 1468 (fifth of 5 numbers)"
Includes bibliographical references (p. 131-132)
Description and Table of Contents
Description
Given a compact Lie group G and a commutative orthogonal ring spectrum R such that R[G]* = π*(R ? G+) is finitely generated and projective over π*(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 π*(X). Under mild hypotheses, such as X being bounded below and the derived page RE∞ vanishing, this spectral sequence converges strongly to the homotopy π*(XtG) of the G-Tate construction XtG = [EG ? F(EG+, X]G.
Table of Contents
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
by "Nielsen BookData"