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arXiv · 1209.2105

A descent spectral sequence for arbitrary K(n)-local spectra with explicit $E_2$-term

Daniel G. Davis·Tyler Lawson
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Abstract

Let n be any positive integer and p any prime. Also, let X be any spectrum and let K(n) denote the nth Morava K-theory spectrum. Then we construct a descent spectral sequence with abutment pi_*(L_{K(n)}(X)) and E_2-term equal to the continuous cohomology of G_n, the extended Morava stabilizer group, with coefficients in a certain discrete G_n-module that is built from various homotopy fixed point spectra of the Morava module of X. This spectral sequence can be contrasted with the K(n)-local E_n-Adams spectral sequence for pi_*(L_{K(n)}(X)), whose E_2-term is not known to always be equal to a continuous cohomology group.

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Daniel G. Davis, Tyler Lawson. 2013-02-17. A descent spectral sequence for arbitrary K(n)-local spectra with explicit $E_2$-term. https://arxiv.org/abs/1209.2105

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