Brown–Peterson cohomology from Morava $E$ -theory
Brown–Peterson cohomology from Morava $E$ -theory
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来自 Morava $E$ 的 Brown–Peterson 上同调理论
DOI：
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发表时间：
2015
影响因子：
1.8
通讯作者：
Nathaniel J. Stapleton
中科院分区：
文献类型：
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作者：
T. Barthel;Nathaniel J. Stapleton
我们证明 $p$ 完成的 Brown-Peterson 谱是 Morava $E$ 理论谱的产物的缩回。因此，我们将 Kashiwabara 以及 Ravenel、Wilson 和 Yagita 的结果从空间推广到谱，并推断出好群的概念是由 Brown-Peterson 上同调决定的。此外，我们表明某些有限群的 Morava $E$ 理论的有理因式分解整体上满足具有高度无关指数的有界挠率，从而将这些因式分解提升为此类群的有理化 Brown-Peterson 上同调。
We prove that the $p$ -completed Brown–Peterson spectrum is a retract of a product of Morava $E$ -theory spectra. As a consequence, we generalize results of Kashiwabara and of Ravenel, Wilson and Yagita from spaces to spectra and deduce that the notion of a good group is determined by Brown–Peterson cohomology. Furthermore, we show that rational factorizations of the Morava $E$ -theory of certain finite groups hold integrally up to bounded torsion with height-independent exponent, thereby lifting these factorizations to the rationalized Brown–Peterson cohomology of such groups.