论文标题
P-ADIC曲线功能字段的统一组的局部全球原理
Local-Global Principle for Unitary Groups Over Function Fields of p-adic Curves
论文作者
论文摘要
令k为p-adic场，f曲线的函数字段在k上。令g为经典类型的F上的连接线性代数组。假设Prime P是G的良好质量。那么，我们证明，G超过F下的投影性均匀空间满足了f离散估值的理性观点的本地全球原则。如果g是一个半简单的群体，则与F相互联系，那么我们还证明，g下的主要均匀空间满足了F的分离估值，这满足了f的本地全球原则。
Let K be a p-adic field and F the function field of a curve over K. Let G be a connected linear algebraic group over F of classical type. Suppose the prime p is a good prime for G. Then we prove that projective homogeneous spaces under G over F satisfy a local global principle for rational points with respect to discrete valuations of F . If G is a semisimple simply connected group over F , then we also prove that principal homogeneous spaces under G over F satisfy a local global principle for rational points with respect to discrete valuations of F.
