The first cohomology group of the generalized Morava stabilizer algebra

Authors:
Hirofumi Nakai and Douglas C. Ravenel

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1629-1639

MSC (2000):
Primary 55P42, 55T15; Secondary 14L05, 20Jxx

Published electronically:
September 19, 2002

MathSciNet review:
1950296

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Abstract | References | Similar Articles | Additional Information

Abstract: There exists a -local spectrum with = . Its Adams-Novikov -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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To appear.**[NRb]**H. Nakai and D. C. Ravenel.

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To appear in Osaka J. Math.**[NY]**H. Nakai and D. Yoritomi.

The structure of the general chromatic -term for .

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In D. M. Davis, editor,*Recent Progress in Homotopy Theory*, volume 293 of*Contemporary Mathematics*, pages 251-284, Providence, Rhode Island, 2002. American Mathematical Society.**[Shia]**Katsumi Shimomura,*The homotopy groups of the 𝐿₂-localized Mahowald spectrum 𝑋⟨1⟩*, Forum Math.**7**(1995), no. 6, 685–707. MR**1359422**, 10.1515/form.1995.7.685**[Shic]**K. Shimomura.

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Additional Information

**Hirofumi Nakai**

Affiliation:
Oshima National College of Maritime Technology, 1091-1 komatsu Oshima-cho Oshima-gun, Yamaguchi 742-2193, Japan

Email:
nakai@c.oshima-k.ac.jp

**Douglas C. Ravenel**

Affiliation:
Department of Mathematics, University of Rochester, Rochester, New York 14627

Email:
drav@math.rochester.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06718-7

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 DMS-9802516

Communicated by:
Paul Goerss

Article copyright:
© Copyright 2002
American Mathematical Society