Cohomology of the Morava stabilizer group through the duality resolution at 𝑛=𝑝=2

Beaudry, Agnès; Bobkova, Irina; Goerss, Paul; Henn, Hans-Werner; Pham, Viet-Cuong; Stojanoska, Vesna

doi:10.1090/tran/8981

Cohomology of the Morava stabilizer group through the duality resolution at $n=p=2$
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by Agnès Beaudry, Irina Bobkova, Paul G. Goerss, Hans-Werner Henn, Viet-Cuong Pham and Vesna Stojanoska;

Trans. Amer. Math. Soc. 377 (2024), 1761-1805

DOI: https://doi.org/10.1090/tran/8981

Published electronically: January 16, 2024

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Abstract:

We compute the continuous cohomology of the Morava stabilizer group with coefficients in Morava $E$-theory, $H^*(\mathbb {G}_2, \mathbf {E}_t)$, at $p=2$, for $0\leq t < 12$, using the Algebraic Duality Spectral Sequence. Furthermore, in that same range, we compute the $d_3$-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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