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

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

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arXiv · 2210.15994

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

Agnes Beaudry·Irina Bobkova·Paul G. Goerss·Hans-Werner Henn·Viet-Cuong Pham·Vesna Stojanoska

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Abstract

We compute the continuous cohomology of the Morava stabilizer group with coefficients in Morava $E$-theory, $H^*(\mathbb{G}_2, E_t)$, 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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Agnes Beaudry, Irina Bobkova, Paul G. Goerss, Hans-Werner Henn, Viet-Cuong Pham, Vesna Stojanoska. 2022-10-28. Cohomology of the Morava stabilizer group through the duality resolution at $n=p=2$. https://arxiv.org/abs/2210.15994

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