Motivic twisted K-theory
Motivic twisted K-theory
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动机扭曲K理论
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
P. Ostvaer
中科院分区：
文献类型：
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作者：
Markus Spitzweck;P. Ostvaer
本文给出了关于权为1的三次动机上同调类的动机扭K-理论的基本性质。动机扭曲K-理论是根据这样的动机上同调类，通过采取回撤沿着通用主BG_m-丛的乘法群方案的分类空间。我们证明了同调模扭K-群的Kuenneth同构，并将后者计算为BG_m的K-理论上K-群的张量积.证明采用了一个亚当斯霍普夫代数胚和一个三阶的动力扭K-理论的Tor-spectral序列。通过将E-无限环谱的概念引入动机同伦理论背景，我们构造了将动机（上）同调群与扭曲K-群联系起来的谱序列。它推广了计算域上概型的代数K-群的各种谱序列。此外，我们构造了动机扭曲K-理论与扭曲周期化有理动机上同调之间的一个Chern特征标，并证明了它是一个有理同构。本文包括一些开放的问题的讨论。
This paper sets out basic properties of motivic twisted K-theory with respect to degree three motivic cohomology classes of weight one. Motivic twisted K-theory is defined in terms of such motivic cohomology classes by taking pullbacks along the universal principal BG_m-bundle for the classifying space of the multiplicative group scheme. We show a Kuenneth isomorphism for homological motivic twisted K-groups computing the latter as a tensor product of K-groups over the K-theory of BG_m. The proof employs an Adams Hopf algebroid and a tri-graded Tor-spectral sequence for motivic twisted K-theory. By adopting the notion of an E-infinity ring spectrum to the motivic homotopy theoretic setting, we construct spectral sequences relating motivic (co)homology groups to twisted K-groups. It generalizes various spectral sequences computing the algebraic K-groups of schemes over fields. Moreover, we construct a Chern character between motivic twisted K-theory and twisted periodized rational motivic cohomology, and show that it is a rational isomorphism. The paper includes a discussion of some open problems.