A descent spectral sequence for arbitrary K(n)-local spectra with explicit $E_2$-term
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.
Cite
@article{arxiv.1209.2105,
title = {A descent spectral sequence for arbitrary K(n)-local spectra with explicit $E_2$-term},
author = {Daniel G. Davis and Tyler Lawson},
journal= {arXiv preprint arXiv:1209.2105},
year = {2013}
}
Comments
Accepted for publication in the Glasgow Mathematical Journal; fixed a typo; added a sentence to the Acknowledgements; and modified the format of the references