A multiplicative Tate spectral sequence for compact Lie group actions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917619351683072 |
|---|---|
| author | Hedenlund, Alice Rognes, John |
| author_facet | Hedenlund, Alice Rognes, John |
| contents | Given a compact Lie group $G$ and a commutative orthogonal ring spectrum $R$ such that $R[G]_* = π_*(R \wedge G_+)$ 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 $E^2$-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 $RE^\infty$ vanishing, this spectral sequence converges strongly to the homotopy $π_*(X^{tG})$ of the $G$-Tate construction $X^{tG} = [\widetilde{EG} \wedge F(EG_+, X)]^G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_09095 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A multiplicative Tate spectral sequence for compact Lie group actions Hedenlund, Alice Rognes, John Algebraic Topology 55T25, 55P91, 16E30 Given a compact Lie group $G$ and a commutative orthogonal ring spectrum $R$ such that $R[G]_* = π_*(R \wedge G_+)$ 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 $E^2$-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 $RE^\infty$ vanishing, this spectral sequence converges strongly to the homotopy $π_*(X^{tG})$ of the $G$-Tate construction $X^{tG} = [\widetilde{EG} \wedge F(EG_+, X)]^G$. |
| title | A multiplicative Tate spectral sequence for compact Lie group actions |
| topic | Algebraic Topology 55T25, 55P91, 16E30 |
| url | https://arxiv.org/abs/2008.09095 |