Advertisement

Mathematische Zeitschrift

, Volume 266, Issue 4, pp 933–951 | Cite as

Comparison of Morava E-theories

  • Takeshi ToriiEmail author
Article

Abstract

We show that the nth Morava E-cohomology group of a finite spectrum with action of the nth Morava stabilizer group can be recovered from the (n + 1)st Morava E-cohomology group with action of the (n + 1)st Morava stabilizer group.

Keywords

Morava E-theory Formal group Morava stabilizer group Chern character 

Mathematics Subject Classification (2000)

55N22 55N20 55S05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ando M., Morava J., Sadofsky H.: Completions of Z/(p)-Tate cohomology of periodic spectra. Geom. Topol. 2, 145–174 (1998) (electronic)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Gross, B.H.: Ramification in p-adic Lie extensions, Journées de Géométrie Algébrique de Rennes (Rennes, 1978), vol. III, pp. 81–102. Astérisque, 65. Soc. Math. France, Paris (1979)Google Scholar
  3. 3.
    Hazewinkel M.: Formal groups and applications. Pure and Applied Mathematics, vol. 78. Academic Press Inc., New York (1978)Google Scholar
  4. 4.
    Hovey, M.: Bousfield localization functors and Hopkins’ chromatic splitting conjecture, The Čech centennial (Boston, MA, 1993), pp. 225–250. Contemp. Math., vol. 181. Amer. Math. Soc., Providence, RI (1995)Google Scholar
  5. 5.
    Hovey M.: Cohomological Bousfield classes. J. Pure Appl. Algebra 103(1), 45–59 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hovey, M., Palmieri, J.H., Strickland, N.P.: Axiomatic stable homotopy theory. Mem. Am. Math. Soc. 128(610) (1997)Google Scholar
  7. 7.
    Hovey, M., Strickland, N.P.: Morava K-theories and localisation. Mem. Am. Math. Soc. 139(666) (1999)Google Scholar
  8. 8.
    Landweber P.S.: Homological properties of comodules over MU*(MU) and BP*(BP). Am. J. Math. 98(3), 591–610 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Lazard M.: Sur les groupes de Lie formels à un paramètre. Bull. Soc. Math. France 83, 251–274 (1955)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Lubin J., Tate J.: Formal moduli for one-parameter formal Lie groups. Bull. Soc. Math. France 94, 49–59 (1966)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Mac Lane S.: Categories for the working mathematician. Graduate Texts in Mathematics, vol. 5. Springer, New York (1998)Google Scholar
  12. 12.
    Matsumura H.: Commutative ring theory. Cambridge Studies in Advanced Mathematics, vol. 8. Cambridge University Press, Cambridge (1989)Google Scholar
  13. 13.
    Miller H.R., Ravenel D.C., Wilson W.S.: Periodic phenomena in the Adams-Novikov spectral sequence. Ann. Math. (2) 106(3), 469–516 (1977)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Milne J.S.: Étale cohomology. Princeton Mathematical Series, vol. 33. Princeton University Press, Princeton (1980)Google Scholar
  15. 15.
    Ravenel D.C.: Nilpotence and periodicity in stable homotopy theory. Appendix C by Jeff Smith. Annals of Mathematics Studies, vol. 128. Princeton University Press, Princeton (1992)Google Scholar
  16. 16.
    Torii T.: On degeneration of formal group laws and application to stable homotopy theory. Am. J. Math. 125, 1037–1077 (2003)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceOkayama UniversityOkayamaJapan

Personalised recommendations