论文标题
$ p $ - 功率扭转的正式团体的扭转点
Ramification of $p$-power torsion points of formal groups
论文作者
论文摘要
让$ p $是一个理性的素数，让$ f $表示有限的，不受影响的扩展为$ \ mathbb {q} _p $，让$ k $是完成$ \ mathbb {q} _p $的最大不受影响的扩展，然后让$ \ yline $ \ ylik $ \ edline {k k} $ nive alge algebraic nive algebraic k $ k $ k $ k $。令$ a $为$ f $定义的亚伯型品种，并以良好的减少，让$ \ Mathcal {a} $表示$ a $ a $ a $ a $ a $ a $ a $ a $ a $ {\ rm spec}（\ mathcal {o} _f）$的néron型号其特殊光纤的身份，即$ a $的正式组。 在这项工作中，我们证明了有关$ \ wideHat {\ Mathcal {a}} $的$ p $ popper扭转点的分支的两个结果。我们的主要结果之一描述了$ \ wideHat {\ Mathcal {a}} $的条件，基础更改为$ \ text {spf}（\ Mathcal {o} _K）$，对于field $ k（\ wideHat {\ wideHat {\ nathcal {\ mathcal {a}}} $ \ wideHat {\ Mathcal {a}} [p] $表示$ p $ -torsion点的组$ \ wideHat {\ Mathcal {a}} $ a $ \ mathcal {o} _ {o} _ {\ edline {k}} $。当$ a $是$ 1 $二维时，当$ a $ a $ a $是某些属2属的jacobian时，该结果将概括为先前的工作。
Let $p$ be a rational prime, let $F$ denote a finite, unramified extension of $\mathbb{Q}_p$, let $K$ be the completion of the maximal unramified extension of $\mathbb{Q}_p$, and let $\overline{K}$ be some fixed algebraic closure of $K$. Let $A$ be an abelian variety defined over $F$, with good reduction, let $\mathcal{A}$ denote the Néron model of $A$ over ${\rm Spec}(\mathcal{O}_F)$, and let $\widehat{\mathcal{A}}$ be the formal completion of $\mathcal{A}$ along the identity of its special fiber, i.e. the formal group of $A$. In this work, we prove two results concerning the ramification of $p$-power torsion points on $\widehat{\mathcal{A}}$. One of our main results describes conditions on $\widehat{\mathcal{A}}$, base changed to $\text{Spf}(\mathcal{O}_K) $, for which the field $K(\widehat{\mathcal{A}}[p])/K$ is a tamely ramified extension where $\widehat{\mathcal{A}}[p]$ denotes the group of $p$-torsion points of $\widehat{\mathcal{A}}$ over $\mathcal{O}_{\overline{K}}$. This result generalizes previous work when $A$ is $1$-dimensional and work of Arias-de-Reyna when $A$ is the Jacobian of certain genus 2 hyperelliptic curves.
