论文标题
关于$ p $ - 亚种字段的整体班级理论
On Integral Class field theory for varieties over $p$-adic fields
论文作者
论文摘要
让$ k $是$ p $ -adic数字的有限扩展，$ \ mathbb q_p $带有整数环$ \ mathcal o_k $，$ \ mathcal x $一个常规方案，适当的，适当的，平坦的，几何性不可避免的$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \米的dimension $ d $ d $ d $ d $ d $ $ \ m natercal x__k $ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $。我们在$ \ Mathcal x_k $的一些假设下表明，局部紧凑型组的互惠同构$ h_ {ar}^{2dd-1}（\ Mathcal x_k，\simeqπ_1^ab}（ab）（ab）cohogy（\ simeq phorytion） integral model $π_1^{ab}(\mathcal X_K)_{W}$ of the abelianized geometric fundamental groups $π_1^{ab}(\mathcal X_K)^{geo}$. After removing the contribution from the base field, the map becomes an isomorphism of finitely generated abelian groups.
Let $K$ be a finite extension of the $p$-adic numbers $\mathbb Q_p$ with ring of integers $\mathcal O_K$, $\mathcal X$ a regular scheme, proper, flat, and geometrically irreducible over $\mathcal O_K$ of dimension $d$, and $\mathcal X_K$ its generic fiber. We show, under some assumptions on $\mathcal X_K$, that there is a reciprocity isomorphism of locally compact groups $H_{ar}^{2d-1}(\mathcal X_K, \mathbb Z(d)) \simeq π_1^{ab}(\mathcal X_K)_{W}$ from a new cohomology theory to an integral model $π_1^{ab}(\mathcal X_K)_{W}$ of the abelianized geometric fundamental groups $π_1^{ab}(\mathcal X_K)^{geo}$. After removing the contribution from the base field, the map becomes an isomorphism of finitely generated abelian groups.
