论文标题
通过K理论和中央扩展的驯服Hilbert符号
The tame Hilbert symbol via K-theory and central extensions
论文作者
论文摘要
让$ k $是一个混合特征的本地领域，其残留场具有基数$ q $，让$ n $为整数划分$ q-1 $。在本文档的第一部分中，我们构建了$ k $ - 理论增强$ n $ th power besitue符号$ k^\ times \ times k^\ times k^\ times \rightarrowμ_n$。在第二部分中，我们按$μ_n$构造了$ gl_m（k）$的中央扩展名，并根据使用$ m = 1 $的扩展定义的符号来表达$ n $ th $ th power残留符号。我们的构造都依赖于有限自由指向的$μ_n$ set的研究。
Let $K$ be a mixed characteristic local field whose residue field has cardinality $q$, and let $n$ be an integer dividing $q-1$. In the first part of this document we construct a $K$-theoretic enhancement of the $n$-th power residue symbol $K^\times \times K^\times \rightarrow μ_n$. In the second part we construct central extensions of $GL_m(K)$ by $μ_n$ and we express the $n$-th power residue symbol in terms of a symbol defined using the extension obtained for $m=1$. Our constructions both rely on the study of finite free pointed $μ_n$-sets.
