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Liftings of formal groups and the Artinian completion of \(v_ n^{- 1}BP\). (English) Zbl 0729.55002
Let \(E_ n\) be the complex oriented generalized cohomology theory obtained by truncating (localized) Brown-Peterson cohomology, BP, and localizing at the last generator. Thus \(BP(pt)={\mathbb{Z}}_{(p)}[\nu_ 1,\nu_ 2,...],\) \(E_ n(pt)={\mathbb{Z}}_{(p)}[\nu_ 1,...,\nu_{n- 1}][\nu_ n,\nu_ n^{-1}],\) where the \(\nu_ i\) are the standard generators. It is known that \(BP[\nu_ n^{-1}]\) cannot be a product of suspension of \(E_ n\) in the multiplicative sense. However, Ravenel conjectured that such a splitting might happen after suitable completions. In this paper the authors establish this result. To do this they use formal groups; in particular they study to this end the problem of lifting p-typical formal group laws and their strict isomorphisms from a characteristic p-algebra k to a local ring A with residue field k.

MSC:
55N22 Bordism and cobordism theories and formal group laws in algebraic topology
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