TY - JOUR
T1 - A descent spectral sequence for arbitrary K(n)-local spectra with explicit e 2-term
AU - Davis, Daniel G.
AU - Lawson, Tyler
PY - 2014/5
Y1 - 2014/5
N2 - Let n be any positive integer and p be 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 π* (LK(n) (X)) and E 2-term equal to the continuous cohomology of Gn , the extended Morava stabilizer group, with coefficients in a certain discrete Gn -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 En -Adams spectral sequence for π* (LK(n) (X)), whose E 2-term is not known to always be equal to a continuous cohomology group.
AB - Let n be any positive integer and p be 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 π* (LK(n) (X)) and E 2-term equal to the continuous cohomology of Gn , the extended Morava stabilizer group, with coefficients in a certain discrete Gn -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 En -Adams spectral sequence for π* (LK(n) (X)), whose E 2-term is not known to always be equal to a continuous cohomology group.
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U2 - 10.1017/S001708951300030X
DO - 10.1017/S001708951300030X
M3 - Article
AN - SCOPUS:84888422993
SN - 0017-0895
VL - 56
SP - 369
EP - 380
JO - Glasgow Mathematical Journal
JF - Glasgow Mathematical Journal
IS - 2
ER -