The Chromatic Ext Groups

Authors:
Ippei Ichigi, Hirofumi Nakai and Douglas C. Ravenel

Journal:
Trans. Amer. Math. Soc. **354** (2002), 3789-3813

MSC (2000):
Primary 55T99; Secondary 55Q51

DOI:
https://doi.org/10.1090/S0002-9947-02-02991-4

Published electronically:
April 23, 2002

MathSciNet review:
1911522

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We compute a certain Ext group related to the chromatic spectral sequence for , the spectrum whose -homology is for each . The answer we get displays a kind of periodicity not seen in the corresponding computation for the sphere spectrum.

**[DHS88]**E. Devinatz, M. J. Hopkins, and J. H. Smith.

Nilpotence and stable homotopy theory.*Annals of Mathematics*, 128:207-242, 1988. MR**89m:55009****[KS]**Y. Kamiya and K. Shimomura.

The homotopy groups .*Hiroshima Math. J.*, 31:391-408, 2001.**[MRW77]**H. R. Miller, D. C. Ravenel, and W. S. Wilson.

Periodic phenomena in the Adams-Novikov spectral sequence.*Annals of Mathematics*, 106:469-516, 1977. MR**56:16626****[MW76]**H. R. Miller and W. S. Wilson.

On Novikov's mod an invariant prime ideal.*Topology*, 15:131-141, 1976. MR**55:6410****[NR]**H. Nakai and D. C. Ravenel.

The structure of the general chromatic -term and , preprint at`http://www.``math.rochester.edu/u/drav/preprints.html`.**[Rav]**D. C. Ravenel.

The method of infinite descent in stable homotopy theory I.

To appear in Proceeding of the JAMI Conference on Homotopy Theory, preprint at`http://www.math.rochester.edu/u/drav/preprints.html`.**[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 Adams-Novikov 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 193-209, Providence, Rhode Island, 2000. American Mathematical Society. MR**2002b:55024****[Shi]**K. Shimomura.

The homotopy groups .

to appear.

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC (2000):
55T99,
55Q51

Retrieve articles in all journals with MSC (2000): 55T99, 55Q51

Additional Information

**Ippei Ichigi**

Affiliation:
Department of Mathematics, Kochi University, Kochi 780-8520, Japan

Email:
95sm004@math.kochi-u.ac.jp

**Hirofumi Nakai**

Affiliation:
Department of Mathematics, Oshima National College of Maritime Technology, Oshima, Japan

Email:
nakai@c.osima-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/S0002-9947-02-02991-4

Received by editor(s):
December 1, 2001

Published electronically:
April 23, 2002

Additional Notes:
The third author acknowledges support from NSF grant DMS-9802516.

Article copyright:
© Copyright 2002
American Mathematical Society