BP operations and Morava's extraordinaryK-theories
BP operations and Morava's extraordinaryK-theories
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BP 运营和 Morava 非凡的 K 理论
DOI：
10.1007/bf01214408
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发表时间：
1975
影响因子：
0.8
通讯作者：
W. Stephen Wilson
中科院分区：
文献类型：
--
作者：
David Copeland Johnson;W. Stephen Wilson
在一系列的文件[17 - 19] Morava使用一个无限序列的非凡的K-理论给一个优雅的结构定理的复杂cobordism有限复杂。摩拉瓦的大部分理论都嵌入了一个相当复杂的代数环境。在我们试图了解他的工作，我们发现更传统的代数拓扑证明他的许多成果。此外，我们的方法为摩拉瓦总体计划做出了新的贡献。我们希望本文将有助于使摩拉瓦的工作更容易和缓解之间的过渡标准代数拓扑和摩拉瓦的论述。Morava被迫在他的代数设置中始终使用复配边法MU *（）。我们可以直接使用布朗-彼得森同调，其中我们正在研究的许多现象更加透明。BP表示固定素数p [-1，7，21]处的Brown-Peterson谱。这个谱给出了一个乘法同调理论BP，（），其系数环BP，= 9（p~1，...，v. 7. (Zcp)多项式生成元v的维数是2（p "-1）。BP的运算环，BP *（BP），在BP上运算，= BP，（S~1）我们方法的第一个好处之一是不变素理想定理的简单直接证明。
In a series of papers [17-19] Morava uses an infinite sequence of extraordinary K-theories to give an elegant structure theorem for the complex cobordism of a finite complex. Much of Morava's theory is embedded in a rather sophisticated algebraic setting. In our attempt to understand his work, we have found more conventional algebraic topological proofs of many of his results. Also, our approach has yielded new contributions to the general Morava program. We hope this paper will help make Morava's work more accessible and ease the transition between standard algebraic topology and Morava's exposition. Morava is forced by his algebraic setting to work throughout with complex cobordism, MU*(). We can work directly with Brown-Peterson homology where many of the phenomena we are studying are more transparent. BP denotes the Brown-Peterson spectrum at a fixed prime p [-1, 7, 21]. This spectrum gives a multiplicative homology theory, BP,(), with coefficient ring BP,= 9 (p~ Iv 1...., v..... 7.(Zcp) is the ring of integers localized at the prime p. The dimension of the polynomial generator v, is 2 (p"-1).) The operation ring for BP, BP*(BP), operates on BP,= BP,(S~ One of the first benefits of our approach was an easy direct proof of the invariant prime ideal theorem.