Memoirs of the American Mathematical Society A Multiplicative Tate Spectral Sequence for Compact Lie Group Actions

Name: Memoirs of the American Mathematical Society A Multiplicative Tate Spectral Sequence for Compact Lie Group Actions
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Bol 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). 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 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 vanishing, this spectral sequence converges strongly to the homotopy π *(XtG) of the G-Tate construction X tG = [ EG ? F( EG+, X] G.

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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). 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 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 vanishing, this spectral sequence converges strongly to the homotopy π *(XtG) of the G-Tate construction X tG = [ EG ? F( EG+, X] G.

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