Let K be a complete discretely valued field with residue field k and F be a function field of a curve over K. Let L/F be a Galois extension of degree n. If n is coprime to char(k), then under some assumptions on k(e.g. k is algebraically closed or a finite field) and on the geometry of the curve, we show that there is a local-global principle with respect to discrete valuations for the norms from the extension L/F.

中文翻译：

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半全局域上规范一环的局部全局原则

设 K 是一个具有残差场 k 的完全离散值域，F 是 K 上曲线的函数域。设 L/F 是 n 次的伽罗瓦扩展。如果 n 是 char(k) 的互质，那么在对 k（例如 k 是代数闭或有限域）和曲线几何的一些假设下，我们表明存在关于离散估值的局部全局原理对于来自扩展 L/F 的规范。