论文标题
在Bloch的地图上，用于扭转循环在非关闭场上
On Bloch's map for torsion cycles over non-closed fields
论文作者
论文摘要
我们将Bloch的地图概括为从代数闭合字段到任意字段的扭转循环。虽然Bloch在代数封闭的字段上的地图对零循环和编辑循环的最高循环含量是注入性的，但我们表明，对任意字段的概括仅是对编码循环的概括，最多只能对零循环的循环进行注入。我们的结果意味着，詹森（Jannsen）在积分$ \ ell $ - ad的连续étale共同体中的周期类图通常不是在有限生成的字段上对扭转零周期的注入。这回答了Scavia和Suzuki的问题。
We generalize Bloch's map on torsion cycles from algebraically closed fields to arbitrary fields. While Bloch's map over algebraically closed fields is injective for zero-cycles and for cycles of codimension at most two, we show that the generalization to arbitrary fields is only injective for cycles of codimension at most two but in general not for zero-cycles. Our result implies that Jannsen's cycle class map in integral $\ell$-adic continuous étale cohomology is in general not injective on torsion zero-cycles over finitely generated fields. This answers a question of Scavia and Suzuki.
