Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Roots of unity and the Adams-Novikov spectral sequence for formal $ A$-modules


Author: Keith Johnson
Journal: Trans. Amer. Math. Soc. 323 (1991), 715-726
MSC: Primary 55T25; Secondary 55N22
DOI: https://doi.org/10.1090/S0002-9947-1991-0987163-3
MathSciNet review: 987163
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The cohomology of a Hopf algebroid related to the Adams-Novikov spectral sequence for formal $ A$-modules is studied in the special case in which $ A$ is the ring of integers in the field obtained by adjoining $ p$th roots of unity to $ {\widehat{\mathbb{Q}}_p}$, the $ p$-adic numbers. Information about these cohomology groups is used to give new proofs of results about the $ {E_2}$ term of the Adams spectral sequence based on $ 2$-local complex $ K$-theory, and about the odd primary Kervaire invariant elements in the usual Adams-Novikov spectral sequence.


References [Enhancements On Off] (What's this?)

  • [AHS] J. F. Adams, A. S. Harris, and R. M. Switzer, Hopf algebras of cooperations for real and complex $ K$-theory, Proc. London Math. Soc. (3) 23 (1971), 385-408. MR 0293617 (45:2694)
  • [B] A. K. Bousfield, On the homotopy theory of $ K$-local spectra at an odd prime, Amer. J. Math. 107 (1985), 895-932. MR 796907 (87c:55010)
  • [J] K. Johnson, The Conner-Floyd map for formal $ A$-modules, Trans. Amer. Math. Soc. 302 (1987), 319-332. MR 887512 (88g:55035)
  • [K] W. Kreuger, The $ 2$-primary $ K$-theory Adams spectral sequence, J. Pure Appl. Algebra 36 (1985), 143-158. MR 787169 (87c:55018)
  • [R1] D. C. Ravenel, The non-existence of odd primary Arf invariant elements in stable homotopy theory, Proc. Cambridge Philos. Soc. 83 (1978), 429-443. MR 0474291 (57:13938)
  • [R2] -, Localization with respect to certain periodic homology theories, Amer. J. Math. 106 (1984), 351-414. MR 737778 (85k:55009)
  • [R3] -, Formal $ A$-modules and the Adams Novikov spectral sequence, J. Pure Appl. Algebra 32 (1984), 327-345. MR 745362 (86a:55023)
  • [R4] -, Complex cobordism and stable homotopy groups of spheres, Academic Press, New York, 1986. MR 860042 (87j:55003)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 55T25, 55N22

Retrieve articles in all journals with MSC: 55T25, 55N22


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1991-0987163-3
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society