We study a local to global principle for certain higher zero-cycles over global fields. We thereby verify a conjecture of Colliot-Th\'el\`ene for these cycles. Our main tool are the Kato conjectures proved by Jannsen, Kerz and Saito. Our approach also allows to reprove the ramified global class field theory of Kato and Saito. Finally, we apply the Kato conjectures to study the $p$-adic cycle class map over henselian discrete valuation rings of mixed characteristic and to deduce finiteness theorems for arithmetic schemes in low degree.

中文翻译：

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更高零周期的局部到全局原理

我们研究了全局域上某些更高零周期的局部到全局原理。因此，我们验证了对这些循环的 Colliot-Th\'el\`ene 的猜想。我们的主要工具是由 Jannsen、Kerz 和 Saito 证明的 Kato 猜想。我们的方法还允许反驳 Kato 和 Saito 的分支全局类场理论。最后，我们应用加藤猜想来研究混合特征的亨塞利离散估值环上的$p$-adic 循环类映射，并推导出低阶算术方案的有限性定理。