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A DESCENT SPECTRAL SEQUENCE FOR ARBITRARY K(n)-LOCAL SPECTRA WITH EXPLICIT E2-TERM

Published online by Cambridge University Press:  13 August 2013

DANIEL G. DAVIS  and
TYLER LAWSON
DANIEL G. DAVIS
Affiliation:
Department of Mathematics, University of Louisiana at Lafayette, 217 Maxim Doucet Hall, P.O. Box 41010, Lafayette, LA, 70504USA e-mail: dgdavis@louisiana.edu
TYLER LAWSON
Affiliation:
Department of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, MN, 55455USA e-mail: tlawson@math.umn.edu
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Abstract

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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 E2-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 E2-term is not known to always be equal to a continuous cohomology group.

Keywords

Primary 55P4255T1555Q51

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 2 , May 2014 , pp. 369 - 380
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

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