ISOTROPIC MOTIVES
ISOTROPIC MOTIVES
复制标题
各向同性动机
DOI：
--
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发表时间：
2019
影响因子：
0.9
通讯作者：
A. Vishik
中科院分区：
文献类型：
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作者：
A. Vishik
本文介绍了Voevodsky动机范畴的局部版本，
$mathbb{F} _p$
- 域k上的系数，由k的k生成的扩展参数化。我们引入所谓的灵活的领域，通道是保守的动机。我们证明，在灵活的领域，构造的本地motivic类别比全球的一个更简单，更让人想起一个拓扑对应。这提供了方便的“本地”不变量，从中可以读取motivic信息。我们计算一个点的局部动机上同调，
$p=2$
研究一下当地的周族动机我们引入了局部Chow群，并猜想在柔性域上，这些群应该与Chow群模数值等价，
$mathbb{F} _p$
系数，这意味着当地的周动机与数值周动机相吻合。我们证明了这一猜想在各种情况下。
Abstract In this article we introduce the local versions of the Voevodsky category of motives with
$mathbb{F} _p$
-coefficients over a field k, parametrized by finitely generated extensions of k. We introduce the so-called flexible fields, passage to which is conservative on motives. We demonstrate that, over flexible fields, the constructed local motivic categories are much simpler than the global one and more reminiscent of a topological counterpart. This provides handy ‘local’ invariants from which one can read motivic information. We compute the local motivic cohomology of a point for
$p=2$
and study the local Chow motivic category. We introduce local Chow groups and conjecture that over flexible fields these should coincide with Chow groups modulo numerical equivalence with
$mathbb{F} _p$
-coefficients, which implies that local Chow motives coincide with numerical Chow motives. We prove this conjecture in various cases.