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Multiplicative Tate Spectral Sequence for Compact Lie Group Actions

Hedenlund, Alice Rognes John
Heftet / 2024 / Engelsk

Product details

ISBN
9781470468781
Published
2024-05-31
Publisher
American Mathematical Society
Weight
118 gr
Height
254 mm
Width
178 mm
Age
P, 06
Language
Product language
Engelsk
Format
Product format
Heftet
Number of pages
134

Author
Hedenlund, Alice
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

Hedenlund, Alice Rognes John
Heftet / 2024 / Engelsk
Hedenlund, Alice Rognes John
Heftet / 2024 / Engelsk
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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.
Read more
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).
Read more
  • 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
    • Read more

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    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.
    Read more
    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).
    Read more
  • 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
    • Read more

    Product details

    ISBN
    9781470468781
    Published
    2024-05-31
    Publisher
    American Mathematical Society
    Weight
    118 gr
    Height
    254 mm
    Width
    178 mm
    Age
    P, 06
    Language
    Product language
    Engelsk
    Format
    Product format
    Heftet
    Number of pages
    134

    Author
    Hedenlund, Alice
    Rognes John

    Biographical note

    Alice Hedenlund, University of Oslo, Norway.

    John Rognes, University of Oslo, Norway.

    Related products