Advertisement

On p-Adic Topological K-Theory

Chapter
Part of the NATO ASI Series book series (ASIC, volume 407)

Abstract

An exposition of the p-adic approach to topological K-theory is given, based on some simple facts about power series over the p-adic integers. As an application, the cohomology of certain spaces attached to p-adic L-functions is computed. These spaces are related to the algebraic K-theory of the integers.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adams, J.F., Stable homotopy theory, Lecture Notes in Mathematics Vol. 3, Springer, New York 1964.Google Scholar
  2. Adams, J.F., Infinite Loop Spaces, Annals of Math. Study 90, Princeton Univeristy Press, 1978. Atiyah, M.F., and Tall, Group representations, a-rings and the J-homomorphism, Topology 8 (1969), 253 - 297.Google Scholar
  3. Clarke, F., Self maps of BU, Math. Proc. Cambridge Phil. Soc. 89 (1981), 491 - 500.zbMATHCrossRefGoogle Scholar
  4. Demazure, M., Lectures on p-divisible groups, Springer-Verlag, New York, 1972.zbMATHCrossRefGoogle Scholar
  5. Dwyer, W. and Friedlander, E., Conjectural calculations of general linear group homology, in Applications of Algebraic K-theory to Algebraic Geometry and Number Theory, Contemp. Math. 55 Part 1 (1986), 135 - 147.MathSciNetGoogle Scholar
  6. Hopkins, M., Lecture at the Adams Memorial Symposium, July 1990.Google Scholar
  7. Husemoller, D., The structure of the Hopf algebra H * BU over a Z(P)-algebra, Amer. J. Math. 43 (1971), 329 - 349.MathSciNetCrossRefGoogle Scholar
  8. Iwasawa, K., Lectures on p-adic L-functions, Annals of Math. Studies no. 74, Princeton University Press, Princeton, New Jersey, 1972.Google Scholar
  9. Lance, T., Local H-maps of classifying spaces, Trans. Amer. Math. Soc. 254 (1979), 195 - 215.MathSciNetzbMATHGoogle Scholar
  10. Lance, T., Local H-maps of BU and applications to smoothing theory, Trans. Amer. Math. Soc. 309 (1988), 391 - 424.MathSciNetzbMATHGoogle Scholar
  11. Madsen, I., Snaith, V., and Tornehave, J., Infinite loop maps in geometric topology, Math. Proc. Comb. Phil. Soc. 81 (1977), 399 - 430.MathSciNetzbMATHCrossRefGoogle Scholar
  12. Mitchell, S.A., On the Lichtenbaum-Quillen conjectures from a stable homotopy-theoretic viewpoint, preprint 1990.Google Scholar
  13. Serre, J.P., Classes de corps cyclotomiques (d’apres K. Iwasawa), Sem. Bourbaki 1958, Exp. no. 174, llpp.Google Scholar
  14. Serre, J.P., Local fields, Springer-Verlag, New York, 1979.zbMATHGoogle Scholar
  15. Sullivan, D., Genetics of homotopy theory and the Adams conjecture, Annals of Math. 100 (1974), 1 - 79.zbMATHCrossRefGoogle Scholar
  16. Washington, L., Introduction to Cyclotomic Fields, Springer-Verlag, 1982.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of WashingtonSeattleUSA

Personalised recommendations