K-理论下降和一个运动的Atiyah-Segal定理
K-theoretic descent and a motivic Atiyah-Segal theorem
摘要：
本文讨论了我们的一个猜想：应用于几何域的绝对伽罗瓦群的表示谱的导出完备构造等价于域的代数K理论.我们证明了p-adic形式的完备化构造可以被解释为包含在一个代数闭域上的某个pro-方案的K-理论。为了构造这种群，我们利用了几何域上的绝对伽罗瓦群的一个特殊性质，即全挠自由性，本文还包含了这类群的表示论的一些性质.
英文摘要：
This paper concerns our earlier conjecture about the equivalence of a derived completion construction applied to the representation spectrum of the absolute Galois group of a geometric field is equivalent to the algebraic K-theory of the field. We prove that the p-adic version of the derived completion construction can be interpreted as the K-theory of a certain pro-scheme over an algebraically closed field contained within the field. In order to make this construction, we use a special property of absolute Galois groups of geometric field, namely that of total torsion freeness, and the paper also contains some poperties of the representation theory of such groups.
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