论文标题
在本地领域的驯服班级理论
Tame class field theory over local fields
论文作者
论文摘要
对于准标准方案$ x $承认在残留特征的本地领域$ p> 0 $承认平稳的压实，我们构建了从温和的班级组到$ x $的Abelian Tame Etale基本组的连续互惠同构。我们描述了其内核和Cokernel的质量到$ p $。 这概括了Jannsen-Saito和Forre的本地领域的较高维度未受到的类领域理论。我们还证明了Abelian Tame Etale基本组的几何部分的有限定理，将Grothendieck和Yoshida的结果推广为未受到的基本组的结果。
For a quasi-projective scheme $X$ admitting a smooth compactification over a local field of residue characteristic $p > 0$, we construct a continuous reciprocity homomorphism from a tame class group to the abelian tame etale fundamental group of $X$. We describe the prime-to-$p$ parts of its kernel and cokernel. This generalizes the higher dimensional unramified class field theory over local fields by Jannsen-Saito and Forre. We also prove a finiteness theorem for the geometric part of the abelian tame etale fundamental group, generalizing the results of Grothendieck and Yoshida for the unramified fundamental group.
