论文标题
刚性分析性Stein代数组为仿射
Rigid analytic Stein algebraic groups are affine
论文作者
论文摘要
令$ k $为一个完全不繁琐的非架构的非安置田地。给定每个常规函数恒定的代数群体，都超过$ k $，任何刚性的分析功能也被证明是恒定的。因此，只有当相关的$ k $ - 分析空间是斯坦因时，就有一个超过$ k $的代数集团是仿射的；也就是说，它在仿射空间中的刚性分析嵌入可能总是由代数函数选择。可以说是奇怪的是，复数上的相应语句是错误的。
Let $K$ be a complete non-trivially valued non-Archimedean field. Given an algebraic group over $K$ on which every regular function is constant, any rigid analytic function is shown to be constant too. It follows that an algebraic group over $K$ is affine if and only if the associated $K$-analytic space is Stein; that is, rigid analytic embeddings of it in an affine space may always be chosen to be given by algebraic functions. Arguably curiously, the corresponding statement over the complex numbers is false.
