A counterexample to a -analogue

of the chromatic splitting conjecture

Author:
Ethan S. Devinatz

Journal:
Proc. Amer. Math. Soc. **126** (1998), 907-911

MSC (1991):
Primary 55N22, 55Q10

DOI:
https://doi.org/10.1090/S0002-9939-98-04104-5

MathSciNet review:
1422861

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that, if , the -localization of the -localization map is not a split monomorphism in the stable category by exhibiting spectra for which the map is not injective. If and , we show that may be taken to be a two-cell complex in the sense of -local homotopy theory. The question of whether the map splits was asked by Hovey and is in some sense a -analogue of Hopkins' chromatic splitting conjecture.

**[1]**E. S. Devinatz,*The generating hypothesis revisited*, to appear in Stable and Unstable Homotopy, Fields Institute Communications, Amer. Math. Soc., 1997.**[2]**M. Hovey, Bousfield localization functors and Hopkins' chromatic splitting conjecture, The Cech Centennial,*Contemp.Math.*, vol. 181, Amer. Math. Soc., Providence, Rhode Island, 1995, pp.225-250. MR**96m:55010****[3]**P. S. Landweber, Homological properties of comodules over and ,*Amer. J. Math.***98**(1976), 591-610. MR**54:11311****[4]**H. R. Miller, D. C. Ravenel, and W. S. Wilson, Periodic phenomena in the Adams-Novikov spectral sequence,*Ann. of Math.***106**(1977), 469-516. MR**56:16626****[5]**D. C. Ravenel, Localization with respect to certain periodic homology theories,*Amer. J. Math.***106**(1984), 351-414. MR**85k:55009****[6]**D. C. Ravenel, Nilpotence and Periodicity in Stable Homotopy Theory,*Ann. of Math. Stud. 128*, Princeton University Press, Princeton, 1992. MR**94b:55015**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
55N22,
55Q10

Retrieve articles in all journals with MSC (1991): 55N22, 55Q10

Additional Information

**Ethan S. Devinatz**

Affiliation:
Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195–4350

Email:
devinatz@math.washington.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04104-5

Received by editor(s):
May 7, 1996

Received by editor(s) in revised form:
August 30, 1996

Additional Notes:
Partially supported by the National Science Foundation

Communicated by:
Thomas Goodwillie

Article copyright:
© Copyright 1998
American Mathematical Society