论文标题
循环的各向同性和数值等效性
On isotropic and numerical equivalence of cycles
论文作者
论文摘要
我们研究了猜想，声称在灵活的字段上，各向同性的食物组与数值盘组相吻合（带有$ {\ bbb {f}} _ p $ -coefficients）。该猜想对于理解各向同性动机类别的结构以及Voevodsky动机类别的张量三角谱的结构至关重要。我们证明了新案例范围的猜想。特别是，我们表明，对于给定品种$ x $，它具有足够大的素数$ p $。我们还证明了$ p $ -Adic类似物。这允许将$ ch（x）$中的数字琐碎类解释为$ p^{\ infty} $ - 各向异性。
We study the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with ${\Bbb{F}}_p$-coefficients). This conjecture is essential for understanding the structure of the isotropic motivic category and that of the tensor triangulated spectrum of Voevodsky category of motives. We prove the conjecture for the new range of cases. In particular, we show that, for a given variety $X$, it holds for sufficiently large primes $p$. We also prove the $p$-adic analogue. This permits to interpret integral numerically trivial classes in $CH(X)$ as $p^{\infty}$-anisotropic ones.
