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2011 | 9 | 5 | 1074-1087
Tytuł artykułu

Galois theory and Lubin-Tate cochains on classifying spaces

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We consider brave new cochain extensions F(BG +,R) → F(EG +,R), where R is either a Lubin-Tate spectrum E n or the related 2-periodic Morava K-theory K n, and G is a finite group. When R is an Eilenberg-Mac Lane spectrum, in some good cases such an extension is a G-Galois extension in the sense of John Rognes, but not always faithful. We prove that for E n and K n these extensions are always faithful in the K n local category. However, for a cyclic p-group $C_{p^r } $, the cochain extension $F(BC_{p^r + } ,E_n ) \to F(EC_{p^r + } ,E_n )$ is not a Galois extension because it ramifies. As a consequence, it follows that the E n-theory Eilenberg-Moore spectral sequence for G and BGdoes not always converge to its expected target.
  • University of Glasgow
  • Fachbereich Mathematik der Universität Hamburg
  • [1] Alperin J.L., Local representation theory, Cambridge Stud. Adv. Math., 11, Cambridge University Press, Cambridge, 1986
  • [2] Baker A., Richter B., Galois extensions of Lubin-Tate spectra, Homology, Homotopy Appl., 2008, 10(3), 27–43
  • [3] Bauer T., Convergence of the Eilenberg-Moore spectral sequence for generalized cohomology theories, preprint available at
  • [4] Becker J.C., Gottlieb D.H., The transfer map and fiber bundles, Topology, 1975, 14(1), 1–12
  • [5] Chase S.U., Harrison D.K., Rosenberg A., Galois theory and Galois cohomology of commutative rings, In: Mem. Amer. Math. Soc., 52, American Mathematical Society, Providence, 1965, 15–33
  • [6] Elmendorf A., Kriz I., Mandell M.A., May J.P., Rings, Modules, and Algebras in Stable Homotopy Theory, Math. Surveys Monogr., 47, American Mathematical Society, Providence, 1997
  • [7] Hopkins M.J., Kuhn N.J., Ravenel D.C., Morava K-theories of classifying spaces and generalized characters for finite groups, In: Algebraic Topology, San Feliu de Guíxols, 1990, Lecture Notes in Math., 1509, Springer, Berlin, 1992, 186–209
  • [8] Hopkins M.J., Kuhn N.J., Ravenel D.C., Generalized group characters and complex oriented cohomology theories, J. Amer. Math. Soc, 2000, 13(3), 553–594
  • [9] Hovey M., Strickland N.P., Morava K-Theories and Localisation, Mem. Amer. Math. Soc, 139(666), American Mathematical Society, Providence, 1999
  • [10] Kriz I., Lee K.P., Odd-degree elements in the Morava K(n) cohomology of finite groups, Topology Appl., 2000, 103(3), 229–241
  • [11] Lam T.Y., A First Course in Noncommutative Rings, 2nd ed., Grad. Texts in Math., 131, Springer, New York, 2001
  • [12] Møller J.M., Frobenius categories for Chevalley groups, available at
  • [13] Ravenel D.C., Morava K-theories and finite groups, In: Symposium on Algebraic Topology in honor of José Adem, Oaxtepec, 1981, Contemp. Math., 12, American Mathematical Society, Providence, 1982, 289–292
  • [14] Ravenel D.C., Wilson W.S., The Morava K-theories of Eilenberg-MacLane spaces and the Conner-Floyd conjecture, Amer. J. Math., 1980, 102(4), 691–748
  • [15] Robinson D.J.S., A Course in the Theory of Groups, 2nd ed., Grad. Texts in Math., 80, Springer, New York, 1996
  • [16] Rognes J., Galois Extensions of Structured Ring Spectra, Mem. Amer. Math. Soc, 192(898), American Mathematical Society, Providence, 2008
  • [17] Rognes J., A Galois extension that is not faithful, preprint available at
  • [18] Tate J., Nilpotent quotient groups, Topology, 1964, 3(suppl. 1), 109–111
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