论文标题
可以在$ p $ airpary封闭的字段中解释的一定的半imple群
Definably semisimple groups interpretable in $p$-adically closed fields
论文作者
论文摘要
让$ k $是$ p $ a的封闭场，而每组$ g $则以$ k $解释。我们表明，如果$ g $明确是半imple（即$ g $没有可确定的无限正常阿贝尔亚组），那么存在有限的普通亚组$ h $ $ h $，因此$ g/h $与$ k $ linearear group具有一定的同构。结果在$ \ mathrm {th}（\ Mathbb {q} _p^{an}）$的模型中保持不变。
Let $K$ be a $p$-adically closed field and $G$ a group interpretable in $K$. We show that if $G$ is definably semisimple (i.e. $G$ has no definable infinite normal abelian subgroups) then there exists a finite normal subgroup $H$ such that $G/H$ is definably isomorphic to a $K$-linear group. The result remains true in models of $\mathrm{Th}(\mathbb{Q}_p^{an})$.
