论文标题
连续$ \ ell $ -ADIC共同体中周期类图的非注射率
Non-injectivity of the cycle class map in continuous $\ell$-adic cohomology
论文作者
论文摘要
詹森（Jannsen）询问连续$ \ ell $ - adic的共同体中的理性周期映射是否是配件的，在所有平滑的投射品种上，在素数上有限类型的所有平滑射击品种中，是否是配件的。正如Schreieder最近指出的那样，Jannsen问题的整体版本也令人感兴趣。我们展示了几个示例，表明整体版本的答案通常是负面的。我们的例子也对Chow组的Coniveau过滤以及Schreieder构建的先验Abel-Jacobi图产生了后果。
Jannsen asked whether the rational cycle class map in continuous $\ell$-adic cohomology is injective, in every codimension for all smooth projective varieties over a field of finite type over the prime field. As recently pointed out by Schreieder, the integral version of Jannsen's question is also of interest. We exhibit several examples showing that the answer to the integral version is negative in general. Our examples also have consequences for the coniveau filtration on Chow groups and the transcendental Abel-Jacobi map constructed by Schreieder.
