邀请到更高的局部域，第II部分，第7节：从伽罗瓦群恢复更高的全局和局部域-代数方法
Invitation to higher local fields, Part II, section 7: Recovering higher global and local fields from Galois groups - an algebraic approach
摘要：
伽罗瓦论中的一个主要问题是用给定的绝对伽罗瓦群来刻画域。我们应用K理论的方法来构建估值研究这个问题在各种情况下。作为第一个应用程序，我们得到了一个代数证明的0维情况下格罗滕迪克的anabelian猜想（证明波普），它说，生成的无限领域是确定的，以纯粹不可分扩张，其绝对伽罗瓦群。作为第二个应用程序（这是一个联合工作与Fesenko），我们分析了算术结构领域的绝对伽罗瓦群作为一个更高的维度局部域。
英文摘要：
A main problem in Galois theory is to characterize the fields with a given absolute Galois group. We apply a K-theoretic method for constructing valuations to study this problem in various situations. As a first application we obtain an algebraic proof of the 0-dimensional case of Grothendieck's anabelian conjecture (proven by Pop), which says that finitely generated infinite fields are determined up to purely inseparable extensions by their absolute Galois groups. As a second application (which is a joint work with Fesenko) we analyze the arithmetic structure of fields with the same absolute Galois group as a higher-dimensional local field.
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