COHOMOLOGY OF THE MORAVA STABILIZER GROUP THROUGH THE DUALITY RESOLUTION AT n = p = 2

Agnès Beaudry; Irina Bobkova; Paul G. Goerss; Hans Werner Henn; Viet Cuong Pham; Vesna Stojanoska

doi:10.1090/tran/8981

COHOMOLOGY OF THE MORAVA STABILIZER GROUP THROUGH THE DUALITY RESOLUTION AT n = p = 2

Agnès Beaudry, Irina Bobkova, Paul G. Goerss, Hans Werner Henn, Viet Cuong Pham, Vesna Stojanoska

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We compute the continuous cohomology of the Morava stabilizer group with coefficients in Morava E-theory, H^∗(G2, Et), at p = 2, for 0 ≤ t < 12, using the Algebraic Duality Spectral Sequence. Furthermore, in that same range, we compute the d3-differentials in the homotopy fixed point spectral sequence for the K(2)-local sphere spectrum. These cohomology groups and differentials play a central role in K(2)-local stable homotopy theory.

Original language	English (US)
Pages (from-to)	1761-1805
Number of pages	45
Journal	Transactions of the American Mathematical Society
Volume	377
Issue number	3
DOIs	https://doi.org/10.1090/tran/8981
State	Published - Mar 2024

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General Mathematics
Applied Mathematics

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AU - Goerss, Paul G.

AU - Henn, Hans Werner

AU - Pham, Viet Cuong

AU - Stojanoska, Vesna

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N2 - We compute the continuous cohomology of the Morava stabilizer group with coefficients in Morava E-theory, H∗(G2, Et), at p = 2, for 0 ≤ t < 12, using the Algebraic Duality Spectral Sequence. Furthermore, in that same range, we compute the d3-differentials in the homotopy fixed point spectral sequence for the K(2)-local sphere spectrum. These cohomology groups and differentials play a central role in K(2)-local stable homotopy theory.

AB - We compute the continuous cohomology of the Morava stabilizer group with coefficients in Morava E-theory, H∗(G2, Et), at p = 2, for 0 ≤ t < 12, using the Algebraic Duality Spectral Sequence. Furthermore, in that same range, we compute the d3-differentials in the homotopy fixed point spectral sequence for the K(2)-local sphere spectrum. These cohomology groups and differentials play a central role in K(2)-local stable homotopy theory.

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COHOMOLOGY OF THE MORAVA STABILIZER GROUP THROUGH THE DUALITY RESOLUTION AT n = p = 2

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