A Multiplicative Tate Spectral Sequence for Compact Lie Group Actions
Seiten
2024
American Mathematical Society (Verlag)
978-1-4704-6878-1 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-6878-1 (ISBN)
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).
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.
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.
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
| Erscheinungsdatum | 05.04.2024 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 118 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-4704-6878-6 / 1470468786 |
| ISBN-13 | 978-1-4704-6878-1 / 9781470468781 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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