论文标题
三角动机类别中的同构
Thom isomorphisms in triangulated motivic categories
论文作者
论文摘要
我们表明，当且仅当张张量单位对象所代表的广义动机共同体学理论中，当时，三角动机类别接受了具有额外结构的矢量束的分类thom同构。我们还表明，稳定的$ \ mathbb {a}^1 $衍生的类别不接受定向向量捆绑包的thom同构，更一般而言，对于符号捆绑包。为此，我们计算了动机球频谱的第一个同源束带，并表明该类别的$ \ mathbb {a}^1 $ - 手理学与第二动机hopf map $ν$相对应的班级是nonzero的，这为$ \ thom $ \ m mathbb的合理理论提供了一种障碍。
We show that a triangulated motivic category admits categorical Thom isomorphisms for vector bundles with an additional structure if and only if the generalized motivic cohomology theory represented by the tensor unit object admits Thom classes. We also show that the stable $\mathbb{A}^1$-derived category does not admit Thom isomorphisms for oriented vector bundles and, more generally, for symplectic bundles. In order to do so we compute the first homology sheaves of the motivic sphere spectrum and show that the class in the coefficient ring of $\mathbb{A}^1$-homology corresponding to the second motivic Hopf map $ν$ is nonzero which provides an obstruction to the existence of a reasonable theory of Thom classes in $\mathbb{A}^1$-cohomology.
