论文标题
Rasmussen-Tamagawa猜想的基本变更版本
A Base Change Version of Rasmussen-Tamagawa Conjecture
论文作者
论文摘要
我们证明了Shafarevich猜想的某种统一版本。作为推论，我们证明了拉斯穆森 - 塔川的猜想，用于特定类别的Abelian品种$ a $ a $在数字$ k $ dimension $ g $上定义的，尤其是任何有限的位置$ v $ of $ k $ $ k $，本地化美元$ \ tilde {\ Mathcal {a}} _v $néron型号$ \ MATHCAL {a} _v $ at $ v $是$ v $ at $ v $的一个仿射组方案$ k_v $ at $ v $），并且比二次扩展$ k_v $的差额很好。
We prove a certain uniform version of the Shafarevich Conjecture. As a corollary, we prove the Rasmussen-Tamagawa Conjecture for a particular class of abelian varieties $A$ defined over a number $K$ of dimension $g$ having everywhere potential good reduction, in particular, for any finite place $v$ of $K$ the localization $A_v:=A\times_{\mathrm{Spec}(K)}\mathrm{Spec}(K_v)$ has either good reduction or {\it totally bad reduction} (connected component $\tilde{\mathcal{A}}_v^0$ of the special fibre $\tilde{\mathcal{A}}_v$ of the Néron model $\mathcal{A}_v$ at $v$ is an affine group scheme over the residue field $k_v$ at $v$) and has good reduction over a quadratic extension of $K_v$.
