Motivic cohomology groups are isomorphic to higher chow groups in any characteristic
Motivic cohomology groups are isomorphic to higher chow groups in any characteristic
复制标题
动机上同调群在任何特征上都同构于高级 Chow 群
DOI：
10.1155/s107379280210403x
复制
发表时间：
2002
影响因子：
1
通讯作者：
V. Voevodsky
中科院分区：
文献类型：
--
作者：
V. Voevodsky
在这篇短文中，我们证明了对于任何域上的光滑格式，[3]中定义的动机上同调群与[1]中定义的动机上同调群同构。鉴于[1，命题12.1]，这意味着[3]的动机上同调群同构于更高的Chow群。这一事实以前只有在奇点假设的解决方案下才知道。证明中的新元素是命题4。文[3]中权q的动机复形Z(Q)定义为C∗(Ztr(Gm))[−q]。在文献[1，第8节]中，Friedlander和Suslin定义了复形，我们将记为Ztr(Q)，记为C∗(−(A，0))[Zqui(X，0)]，其中Zqui(X，0)是X上相对零维的等维圈层。在本文中，我们证明了以下结果。
In this short paper we show that the motivic cohomology groups defined in [3] are isomorphic to the motivic cohomology groups defined in [1] for smooth schemes over any field. In view of [1, Proposition 12.1] this implies that motivic cohomology groups of [3] are isomorphic to higher Chow groups. This fact was previously known only under the resolution of singularities assumption. The new element in the proof is Proposition 4. The motivic complex Z(q) of weight q was defined in [3] as C∗(Ztr(G m ))[−q]. In [1, Section 8] Friedlander and Suslin defined complexes, which we will denote Z tr (q), as C∗(zequi(A , 0))[−2q] where zequi(X, 0) is the sheaf of equidimensional cycles on X of relative dimension zero. In this paper we prove the following result.