On the [p]-series in Brown-Peterson homology. (English) Zbl 0632.55002
The author makes a detailed study of the coefficients of the multiplication-by-p series [p](X) for the formal group law of Brown- Peterson homology at the prime p. His main result asserts that each coefficient of [p](X) lies in a product of invariant prime ideals in \(BP_*\), the product containing the coefficient \(a_ s\in BP_{2s}\) depending directly on the p-adic expansion of \(s+1\).
Reviewer: P.Landweber
MSC:
| 55N22 | Bordism and cobordism theories and formal group laws in algebraic topology |
| 55N20 | Generalized (extraordinary) homology and cohomology theories in algebraic topology |
| 57R77 | Complex cobordism (\(\mathrm{U}\)- and \(\mathrm{SU}\)-cobordism) |
References:
| [1] | Hazewinkel, M., A universal formal group and complex cobordism, Bull. Amer. Math. Soc., 81, 930-936 (1975) · Zbl 0315.14017 |
| [2] | Ravenel, D. C., The structure of \(BP_∗\) BP modulo an invariant prime ideal, Topology, 15, 149-153 (1976) · Zbl 0335.55005 |
| [3] | Wilson, W. S., Brown-Peterson Homology: An Introduction and Sampler, (Regional Conference Series in Mathematics, 48 (1982), American Mathematical Society: American Mathematical Society Providence, RI) · Zbl 0518.55001 |
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