论文标题
分裂Milnor-Witt动机及其在纤维束上的应用
Split Milnor-Witt Motives and its Applications to Fiber Bundles
论文作者
论文摘要
我们研究Milnor-Witt动机，这是$ \ mathbb {z}（q）[p] $和$ \ mathbb {z}/η（q）[p] $的有限直接总和。我们表明，对于这种类型的MW-动力，我们可以根据动机共同体学和Witt Coolomology班来确定MW-动力的共同体学课程。我们定义了动机Bockstein的共同体学，并表明它与Witt同胞的亚组相对应，如果MW-MOTIVE分裂如上所述。作为应用程序，我们给出了米尔诺·沃特（Milnor-Witt）动机的分裂公式和完全的旗帜捆绑包。这特别表明，真实完整标志的整体共同体学只有2个扭曲。
We study the Milnor-Witt motives which are a finite direct sum of $\mathbb{Z}(q)[p]$ and $\mathbb{Z}/η(q)[p]$. We show that for MW-motives of this type, we could determine an MW-motivic cohomology class in terms of a motivic cohomology class and a Witt cohomology class. We define the motivic Bockstein cohomology and show that it corresponds to subgroup of Witt cohomology, if the MW-motive splits as above. As an application, we give the splitting formula of Milnor-Witt motives of Grassmannian bundles and complete flag bundles. This in particular shows that the integral cohomology of real complete flags has only 2-torsions.
