论文标题
存在性和二氧稳定性
Existential definability and diophantine stability
论文作者
论文摘要
让$ k $为一个数字字段，让$ l $为$ k $的代数（可能是无限度）的扩展名，让$ o_k $ $ \ $ \ subset $ $ o_l $是他们的整数。假设$ a $是$ k $上定义的阿贝利安品种，因此$ a（k）$是无限的，$ a（l）/a（k）$是扭力组。如果满足以下至少一个条件： 1。$ l $是一个数字字段，2。$ l $是完全真实的，3。$ l $是完全真实字段的二次扩展，然后$ o_k $具有$ o_l $的二磷剂定义。
Let $K$ be a number field, let $L$ be an algebraic (possibly infinite degree) extension of $K$, and let $O_K$ $\subset$ $O_L$ be their rings of integers. Suppose $A$ is an abelian variety defined over $K$ such that $A(K)$ is infinite and $A(L)/A(K)$ is a torsion group. If at least one of the following conditions is satisfied: 1. $L$ is a number field, 2. $L$ is totally real, 3. $L$ is a quadratic extension of a totally real field, then $O_K$ has a diophantine definition over $O_L$.
