论文标题
IwasawaDieudonné功能领域理论
Iwasawa Dieudonné theory of function fields
论文作者
论文摘要
让$ k $是一个特征性$ p $和无限的$γ$的完美领域，第一个可计数$ $ p $组。我们研究了“动机阶级组”的$ p $ - 主要部分，即雅各比式的整个$ p $ - 可见的群体，在任何$γ$ t的$ k $的$γ$ the $ k $中，这些字段超过$ k $，而这些字段在有限的（可能是空的）$σ$的情况下不受限制（可能是空的）$σ$，并且在$σ$ $σ$的每一个地方都被覆盖。当$σ= \ emptyset $和$γ$是免费的$ p $ -Adic Lie Group时，我们获得了渐近公式，这表明$ p $ torsion class clost组计划以一种非常规律的方式生长。在设置$σ\ neq \ emptySet $中，我们获得了类似的渐近公式，用于“物理班级”中的$ p $ torsion，即Jacobian的$ k $ - 差异点，该点概括了Mazur and Wiles的工作，该工作研究了$γ= \ Mathbf {Z} _p $。
Let $k$ be a perfect field of characteristic $p$ and $Γ$ an infinite, first countable pro-$p$ group. We study the behavior of the $p$-primary part of the "motivic class group", i.e. the full $p$-divisible group of the Jacobian, in any $Γ$-tower of function fields over $k$ that is unramified outside a finite (possibly empty) set of places $Σ$, and totally ramified at every place of $Σ$. When $Σ=\emptyset$ and $Γ$ is a torsion free $p$-adic Lie group, we obtain asymptotic formulae which show that the $p$-torsion class group schemes grow in a remarkably regular manner. In the ramified setting $Σ\neq\emptyset$, we obtain a similar asymptotic formula for the $p$-torsion in "physical class groups", i.e. the $k$-rational points of the Jacobian, which generalizes the work of Mazur and Wiles, who studied the case $Γ=\mathbf{Z}_p$.
