Roots of unity and the Adams-Novikov spectral sequence for formal $A$-modules
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- by Keith Johnson PDF
- Trans. Amer. Math. Soc. 323 (1991), 715-726 Request permission
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
- 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 293617, DOI 10.1112/plms/s3-23.3.385
- A. K. Bousfield, On the homotopy theory of $K$-local spectra at an odd prime, Amer. J. Math. 107 (1985), no. 4, 895–932. MR 796907, DOI 10.2307/2374361
- Keith Johnson, The Conner-Floyd map for formal $A$-modules, Trans. Amer. Math. Soc. 302 (1987), no. 1, 319–332. MR 887512, DOI 10.1090/S0002-9947-1987-0887512-X
- Warren M. Krueger, The $2$-primary $K$-theory Adams spectral sequence, J. Pure Appl. Algebra 36 (1985), no. 2, 143–158. MR 787169, DOI 10.1016/0022-4049(85)90067-2
- Douglas C. Ravenel, The non-existence of odd primary Arf invariant elements in stable homotopy, Math. Proc. Cambridge Philos. Soc. 83 (1978), no. 3, 429–443. MR 474291, DOI 10.1017/S0305004100054712
- Douglas C. Ravenel, Localization with respect to certain periodic homology theories, Amer. J. Math. 106 (1984), no. 2, 351–414. MR 737778, DOI 10.2307/2374308
- Douglas C. Ravenel, Formal $A$-modules and the Adams-Novikov spectral sequence, J. Pure Appl. Algebra 32 (1984), no. 3, 327–345. MR 745362, DOI 10.1016/0022-4049(84)90096-3
- Douglas C. Ravenel, Complex cobordism and stable homotopy groups of spheres, Pure and Applied Mathematics, vol. 121, Academic Press, Inc., Orlando, FL, 1986. MR 860042
Additional Information
- © Copyright 1991 American Mathematical Society
- 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