论文标题
半全球田地的赫尔米利亚空间的局部全球原则
Local-global principles for hermitian spaces over semi-global fields
论文作者
论文摘要
让$ k $成为一个完整的离散字段，带有残基字段$ k $和$ f $ the曲线超过$ k $的功能场。令$ a \ in {} _2br（f）$为中央简单代数，任何种类的划分$σ$，$ f_0 = f^σ$。令$ h $为$（a，σ）$和$ g = su（a，σ，h）$的Hermitian空间，如果$σ$是第一类，而$ g = u（a，σ，h）$如果$σ$是第二类。假设$ \ text {char}（k）\ neq 2 $和ind $（a）\ leq 4 $。然后，我们证明，超过$ f_0 $ $ g $ $ g $ $ g $ $ f_0 $的投影性均匀空间满足了$ f $的离散估值的当地全球原则。
Let $K$ be a complete discrete valued field with residue field $k$ and $F$ the function field of a curve over $K$. Let $A \in {}_2Br(F)$ be a central simple algebra with an involution $σ$ of any kind and $F_0 =F^σ$. Let $h$ be an hermitian space over $(A, σ)$ and $G = SU(A, σ, h)$ if $σ$ is of first kind and $G = U(A, σ, h)$ if $σ$ is of second kind. Suppose that $\text{char}(k) \neq 2$ and ind$(A)\leq 4$. Then we prove that projective homogeneous spaces under $G$ over $F_0$ satisfy a local-global principle for rational points with respect to discrete valuations of $F$.
