论文标题
通过动机同源性检测动机
Detecting motivic equivalences with motivic homology
论文作者
论文摘要
让$ k $为一个字段，让$ r $为通勤戒指，并假设$ k $的指数特征在$ r $中是可逆的。在本说明中，我们证明了Voevodsky的三角剖分类别的同构$ \ Mathcal {dm}（k; r）$被动机同源群检测到所有可分离有限生成的$ k $的现场扩展的基础变化。然后从以前的保守性结果来看，这些动机同源群检测到尖锐的动机同义类别中某些空间之间的同构$ \ Mathcal {h}（k）_*$。
Let $k$ be a field, let $R$ be a commutative ring, and assume the exponential characteristic of $k$ is invertible in $R$. In this note, we prove that isomorphisms in Voevodsky's triangulated category of motives $\mathcal{DM}(k;R)$ are detected by motivic homology groups of base changes to all separable finitely generated field extensions of $k$. It then follows from previous conservativity results that these motivic homology groups detect isomorphisms between certain spaces in the pointed motivic homotopy category $\mathcal{H}(k)_*$.
