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Multiplicative Tate Spectral Sequence for Compact Lie Group Actions

Rognes John
Heftet / 2024 / Engelsk

Produktdetaljer

ISBN
9781470468781
Publisert
2024-05-31
Utgiver
Vendor
American Mathematical Society
Vekt
118 gr
Høyde
254 mm
Bredde
178 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
134

Forfatter
Rognes John

Biographical note

Alice Hedenlund, University of Oslo, Norway.

John Rognes, University of Oslo, Norway.

Multiplicative Tate Spectral Sequence for Compact Lie Group Actions

Rognes John
Heftet / 2024 / Engelsk
Rognes John
Heftet / 2024 / Engelsk
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Klikk og hent
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.
Les mer
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).
Les mer
  • 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
    • Les mer

    Relaterte produkter

    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.
    Les mer
    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).
    Les mer
  • 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
    • Les mer

    Produktdetaljer

    ISBN
    9781470468781
    Publisert
    2024-05-31
    Utgiver
    Vendor
    American Mathematical Society
    Vekt
    118 gr
    Høyde
    254 mm
    Bredde
    178 mm
    Aldersnivå
    P, 06
    Språk
    Product language
    Engelsk
    Format
    Product format
    Heftet
    Antall sider
    134

    Forfatter
    Rognes John

    Biographical note

    Alice Hedenlund, University of Oslo, Norway.

    John Rognes, University of Oslo, Norway.

    Relaterte produkter