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

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

doi:10.1090/tran/8981

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

MPS-Authors

/persons/resource/persons297583

Beaudry, Agnès
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons297577

Bobkova, Irina
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons297580

Goerss, Paul G.
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons235422

Henn, Hans-Werner
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons281398

Pham, Viet-Cuong
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons236259

Stojanoska, Vesna
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.48550/arXiv.2210.15994
(プレプリント)

https://doi.org/10.1090/tran/8981
(出版社版)

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引用

Beaudry, A., Bobkova, I., Goerss, P. G., Henn, H.-W., Pham, V.-C., & Stojanoska, V. (2024). Cohomology of the Morava stabilizer group through the duality resolution at n=p=2. Transactions of the American Mathematical Society, 377(3), 1761-1805. doi:10.1090/tran/8981.

引用: https://hdl.handle.net/21.11116/0000-000F-233F-4

要旨

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.