论文标题
$ sl（2，f）$ for Local Fields中的参与式限制的限制
Chabauty limits of groups of involutions in $SL(2,F)$ for local fields
论文作者
论文摘要
我们对$ sl（2，f）$的各种（摘要）差异固定的组的chabauty限制进行了分类，其中$ f $是$ \ mathbb {q} _p $的有限字段扩展，带有$ p \ neq 2 $。为此，我们首先将$ sl（2，f）$上的抽象反应与$ f $ a二次扩展为$ \ mathbb {q} _p $，并证明$ p $ p $ - adic极性分解相对于$ p $ - adic $ sl_2 $的各种子组。然后，我们将chabauty限制分类为：$ sl（2，f）\ subset sl（2，e）$，其中$ e $是$ f $的二次扩展为$ f $，$ sl（2，\ mathbb {r}）\ subset sl sl（2，2，\ mathbb {c}） $ f $ -involution $θ$超过$ sl（2，f）$。
We classify Chabauty limits of groups fixed by various (abstract) involutions over $SL(2,F)$, where $F$ is a finite field-extension of $\mathbb{Q}_p$, with $p\neq 2$. To do so, we first classify abstract involutions over $SL(2,F)$ with $F$ a quadratic extension of $\mathbb{Q}_p$, and prove $p$-adic polar decompositions with respect to various subgroups of $p$-adic $SL_2$. Then we classify Chabauty limits of: $SL(2, F) \subset SL(2,E)$ where $E$ is a quadratic extension of $F$, of $SL(2,\mathbb{R}) \subset SL(2,\mathbb{C})$, and of $H_θ\subset SL(2,F)$, where $H_θ$ is the fixed point group of an $F$-involution $θ$ over $SL(2,F)$.
