A Multiplicative Tate Spectral Sequence for Compact Lie Group Actions Robert Finkel Matanuska-Susitna Valley and Palmer

Matanuska-Susitna Valley and Palmer

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A Multiplicative Tate Spectral Sequence for Compact Lie Group Actions Robert Finkel Matanuska-Susitna Valley and PalmerGiven a compact Lie group G and a commutative orthogonal ring spectrum R such that R[G]* = ?*(R ? G+) is finitely generated and projective over ?*(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 ?*(X). Under mild hypotheses, such as X being bounded below and the derived page RE? vanishing, this spectral sequence