论文标题
四二次超曲面和互动品种的彩色类别
Grothendieck classes of quadric hypersurfaces and involution varieties
论文作者
论文摘要
在本文中，通过将最新的非共同动机理论与经典的动机理论相结合，我们证明，如果两个Quadrics（或更一般而言，两个互动品种）具有相同的Grothendieck类，那么他们甚至具有相同的Clifford代数和同一签名。作为应用程序，我们在许多情况下（例如，当基本场是局部或全局字段）中表明，当且仅当它们是同构时，两个四边形（或更一般而言，更通常是两个互动品种）具有相同的Grothendieck类。
In this article, by combining the recent theory of noncommutative motives with the classical theory of motives, we prove that if two quadrics (or, more generally, two involution varieties) have the same Grothendieck class, then they have the same even Clifford algebra and the same signature. As an application, we show in numerous cases (e.g., when the base field is a local or global field) that two quadrics (or, more generally, two involution varieties) have the same Grothendieck class if and only if they are isomorphic.
