论文标题
ABELIAN几何基本组，用于$ p $ - adic领域的曲线
Abelian geometric fundamental groups for curves over a $p$-adic field
论文作者
论文摘要
对于$ p $ -ADIC字段$ k $上的曲线$ x $，使用S. Bloch和S. S. Saito的类字段理论，我们研究Abelian几何基本基本组$π_1^{\ mathrm {abrm {abrm {abrm {ab}}}（x）特别是，研究了$π_1^{\ mathrm {ab}}（x）^{\ mathrm {geo}} $的子组，该子组对$ x $的几何和$ x $的几何和亚伯封面进行了分类，从而使$ x $的覆盖率允许使用$ x $的特殊模型。在假设$ x $具有$ k $ - 合理点的假设下，$ x $具有很好的减少，其雅各布品种具有良好的普通降低，我们给出了$π_1^{\ mathrm {abrm {abrm {abrm {ab}}}（x）^{\ mathrm {geo {geo}} $的上层和下限。
For a curve $X$ over a $p$-adic field $k$, using the class field theory of $X$ due to S. Bloch and S. Saito we study the abelian geometric fundamental group $π_1^{\mathrm{ab}}(X)^{\mathrm{geo}}$ of $X$. In particular, it is investigated a subgroup of $π_1^{\mathrm{ab}}(X)^{\mathrm{geo}}$ which classifies the geometric and abelian coverings of $X$ which allow possible ramification over the special fiber of the model of $X$. Under the assumptions that $X$ has a $k$-rational point, $X$ has good reduction and its Jacobian variety has good ordinary reduction, we give some upper and lower bounds of this subgroup of $π_1^{\mathrm{ab}}(X)^{\mathrm{geo}}$.
