论文标题
雅克山雀动机措施
Jacques Tits motivic measure
论文作者
论文摘要
在本文中，我们构建了一种新的动机措施，称为$ {\ it jacques} $ $ {\ it tits} $ $ {\ it Itivic} $ $ {\ it measure south} $。作为雅克山雀动机措施的第一个主要应用，我们证明了两个透明的品种（或更一般而言，两个扭曲的格拉曼尼亚品种），与$ 2 $ 2 $ - 托管中央简单代数相关，在肉眼grothendieck圈中具有相同的类别。此外，我们证明，如果两个veri-brauer品种与$ \ {3、4、5、6 \} $的中央简单代数相关，则在Grothendieck品种环中具有相同的类别，那么它们一定是彼此的。作为Jacques山雀动机措施的第二个主要应用，我们证明了两个二次突出（或更一般而言）与尺寸$ 6 $的二次形式相关的二次形式，或与$ i^3（k）= 0 $相同的二级$ k $ k $ k $ k $ k $ i is she is she is is eys grophielie grophieleeck and gropheck and gropheck and gropheck and gropheck and the the the the the the the the the the the the the的任意形式。此外，我们证明后一个主要应用程序还适用于二次超曲面产品。
In this article we construct a new motivic measure called the ${\it Jacques}$ ${\it Tits}$ ${\it motivic}$ ${\it measure}$. As a first main application of the Jacques Tits motivic measure, we prove that two Severi-Brauer varieties (or, more generally, two twisted Grassmannian varieties), associated to $2$-torsion central simple algebras, have the same class in the Grothendieck ring of varieties if and only if they are isomorphic. In addition, we prove that if two Severi-Brauer varieties, associated to central simple algebras of period $\{3, 4, 5, 6\}$, have the same class in the Grothendieck ring of varieties, then they are necessarily birational to each other. As a second main application of the Jacques Tits motivic measure, we prove that two quadric hypersurfaces (or, more generally, two involution varieties), associated to quadratic forms of dimension $6$ or to quadratic forms of arbitrary dimension defined over a base field $k$ with $I^3(k)=0$, have the same class in the Grothendieck ring of varieties if and only if they are isomorphic. In addition, we prove that the latter main application also holds for products of quadric hypersurfaces.
