The first cohomology group of the generalized Morava stabilizer algebra
Authors:
Hirofumi Nakai and Douglas C. Ravenel
Journal:
Proc. Amer. Math. Soc. 131 (2003), 16291639
MSC (2000):
Primary 55P42, 55T15; Secondary 14L05, 20Jxx
Published electronically:
September 19, 2002
MathSciNet review:
1950296
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: There exists a local spectrum with = . Its AdamsNovikov term is isomorphic to
where In this paper we determine the groups for all . Its rank ranges from to depending on the value of .
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 I. Ichigi and K.Shimomura.
The chromatic term . Mem. Fac. Sci. Kochi Univ. (Math.), 21:6371, 2000. MR 2000k:55018
 [INR]
 I. Ichigi, H. Nakai, and D. C. Ravenel.
The chromatic Ext groups . Trans. Amer. Math. Soc., 354:37893813, 2002.
 [KS93]
 N. Kodama and K. Shimomura.
On the homotopy groups of a spectrum related to Ravenel's spectra . J. Fac. Educ. Tottori Univ. (Nat. Sci.), 42:1730, 1993.
 [KS01]
 Y. Kamiya and K. Shimomura.
The homotopy groups . Hiroshima Mathematical Journal, 31:391408, 2001.
 [May66]
 J. P. May.
The cohomology of restricted Lie algebras and of Hopf algebras. Journal of Algebra, 3:123146, 1966. MR 33:1347
 [MM65]
 J. W. Milnor and J. C. Moore.
On the structure of Hopf algebras. Annals of Mathematics, 81(2):211264, 1965. MR 30:4259
 [MR77]
 H. R. Miller and D. C. Ravenel.
Morava stabilizer algebras and the localization of Novikov's term. Duke Mathematical Journal, 44:433447, 1977. MR 56:16613
 [MRW77]
 H. R. Miller, D. C. Ravenel, and W. S. Wilson.
Periodic phenomena in the AdamsNovikov spectral sequence. Annals of Mathematics, 106:469516, 1977. MR 56:16626
 [MS93a]
 M. E. Mahowald and K. Shimomura.
The AdamsNovikov spectral sequence for the localization of a spectrum. Contemporary Mathematics, 146:237250, 1993. MR 94g:55012
 [MS93b]
 H. Mitsui and K. Shimomura.
The Ext groups . J. Fac. Educ. Tottori Univ. (Nat. Sci.), 42:85101, 1993.
 [NRa]
 H. Nakai and D. C. Ravenel.
The method of infinite descent in stable homotopy theory II. To appear.
 [NRb]
 H. Nakai and D. C. Ravenel.
The structure of the general chromatic term and . To appear in Osaka J. Math.
 [NY]
 H. Nakai and D. Yoritomi.
The structure of the general chromatic term for . To appear.
 [Rav86]
 D. C. Ravenel.
Complex Cobordism and Stable Homotopy Groups of Spheres. Academic Press, New York, 1986. Errata available online at http://www.math.rochester.edu/u/drav/mu.html. MR 87j:55003
 [Rav00]
 D. C. Ravenel.
The microstable AdamsNovikov spectral sequence. In D. Arlettaz and K. Hess, editors, Une dégustation topologique [Topological morsels]: homotopy theory in the Swiss Alps (Arolla, 1999), volume 265 of Contemporary Mathematics, pages 193209, Providence, Rhode Island, 2000. American Mathematical Society. MR 2002b:55024
 [Rav02]
 D. C. Ravenel.
The method of infinite descent in stable homotopy theory I. In D. M. Davis, editor, Recent Progress in Homotopy Theory, volume 293 of Contemporary Mathematics, pages 251284, Providence, Rhode Island, 2002. American Mathematical Society.
 [Shia]
 K. Shimomura.
The homotopy groups of the localized mahowald spectrum . Forum Mathematicum, 7:685707. MR 96m:55023
 [Shic]
 K. Shimomura.
The homotopy groups . Recent progress in homotopy theory (Baltimore, MD, 2000), 285297, Contemp. Math., 293, Amer. Math. Soc., Providence, RI, 2002.
 [Shi95]
 K. Shimomura.
Chromatic terms  up to April 1995. J. Fac. Educ. Tottori Univ. (Nat. Sci.), 44:16, 1995.
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Additional Information
Hirofumi Nakai
Affiliation:
Oshima National College of Maritime Technology, 10911 komatsu Oshimacho Oshimagun, Yamaguchi 7422193, Japan
Email:
nakai@c.oshimak.ac.jp
Douglas C. Ravenel
Affiliation:
Department of Mathematics, University of Rochester, Rochester, New York 14627
Email:
drav@math.rochester.edu
DOI:
http://dx.doi.org/10.1090/S0002993902067187
PII:
S 00029939(02)067187
Received by editor(s):
June 14, 2001
Received by editor(s) in revised form:
December 19, 2001
Published electronically:
September 19, 2002
Additional Notes:
The second author acknowledges support from NSF grant DMS9802516
Communicated by:
Paul Goerss
Article copyright:
© Copyright 2002
American Mathematical Society
