p—adic域上单代数群的存在性定理

设k为p-adic域,给出了所有定义在k上,具有不同类型k-指标的单线性代数群的统一构造方法,从而给出了定义在k上单代数群的存在性的统一证明,并且给出了所有定义在k上单线性代数群的k-有理点群的统一构造。

ON EXISTENCE THEOREM OF SIMPLE ALGEBRAIC GROUPS OVER p-ADIC FIELDS

We give a uniform construction of the simple algebraic groups definedover a p-adic field k having the various k-indices and give a uniform construction ofthe simple groups which are the groups of the k-rational points of the simple algebraicgroups defined over k mentioned above.Then we give a uniform proof of existence forsimple algebraic groups defined over k for all k-indices in this note.