论文标题
基础场扩展下的聊天表面算术
Arithmetic of Chatelet surfaces under extensions of base fields
论文作者
论文摘要
对于定义在数字字段上的布置表面，我们研究了两个算术特性，即Hasse原理和弱近似，当传递到基本场的扩展。概括了Y. Liang的结构，我们表明，对于数字字段的任意扩展$ l/k，$，在$ k $上有一个碎屑表面，在$ l/k，$和$ k $的任何中间场上都无法满足薄弱的近似值，而在$ k $上的$ k $ yymedied firtiper firtied field of livemied field $ l'$ l'$，即
For Châtelet surfaces defined over number fields, we study two arithmetic properties, the Hasse principle and weak approximation, when passing to an extension of the base field. Generalizing a construction of Y. Liang, we show that for an arbitrary extension of number fields $L/K,$ there is a Châtelet surface over $K$ which does not satisfy weak approximation over any intermediate field of $L/K,$ and a Châtelet surface over $K$ which satisfies the Hasse principle over an intermediate field $L'$ if and only if $[L' : K]$ is even.
