论文标题
MW-Motivic Sopomology中的投射捆绑捆
Projective Bundle Theorem in MW-Motivic Cohomology
论文作者
论文摘要
我们提出了MW-MOTIVES（分别Chow-Witt Rings）中的投影捆绑捆绑定理的版本，该版本说$ \ widetilde {ch}^*（\ Mathbb {p}（e））$由$ \ widetilde {ch}^*（ch}^*（x）$，$ \ wideTildeLdeLdeLe $ ch^*（x）$和$ sq^2 $用于平滑准标记方案$ x $和vector Bundles $ e $ over $ x $，带有$ e（e^{\ vee}）= 0 \ in H^n（x，x，w（det（e））$，规定为$ _2ch^*（x）= 0 $。 作为应用程序，我们计算了带有光滑中心的爆炸的MW动力。此外，我们讨论了在矢量束的自动形态下，投影束的盘野战赛循环的不变性。
We present a version of projective bundle theorem in MW-motives (resp. Chow-Witt rings), which says that $\widetilde{CH}^*(\mathbb{P}(E))$ is determined by $\widetilde{CH}^*(X)$, $\widetilde{CH}^*(X,det(E)^{\vee})$, $CH^*(X)$ and $Sq^2$ for smooth quasi-projective schemes $X$ and vector bundles $E$ over $X$ with $e(E^{\vee})=0\in H^n(X,W(det(E)))$, provided that $_2CH^*(X)=0$. As an application, we compute the MW-motives of blow-ups with smooth centers. Moreover, we discuss the invariance of Chow-Witt cycles of projective bundles under automorphisms of vector bundles.
