Algebraic Morava K-theories
Algebraic Morava K-theories
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代数 Morava K 理论
DOI：
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发表时间：
2003
期刊：
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通讯作者：
S. Borghesi
中科院分区：
文献类型：
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作者：
S. Borghesi
摘要。对于任意素数q和正整数t，我们构造了具有嵌入k“∈”的域k上方案的稳定同伦范畴中的谱k(t)。在经典同伦理论中，k(t)的向量的实现被称为Morava k理论。其代数内容在于，这些谱被定义为一个塔的同伦极限，该塔的共纤维是动力学Eilenberg-MacLane谱的适当悬架，而动力学Eilenberg-MacLane谱在方案的稳定同伦范畴中表示动力学上同伦。
Abstract.For any prime q and positive integer t, we construct a spectrum k(t) in the stable homotopy category of schemes over a field k equipped with an embedding k↪ℂ. In classical homotopy theory, the ℂ realization of k(t) is known as Morava K-theory. The algebraic content lies in the fact that these spectra are defined as the homotopy limit of a tower whose cofibers are appropriate suspensions of the motivic Eilenberg-MacLane spectra, which are known to represent motivic cohomology in the stable homotopy category of schemes.