Gal(Qp/Qp) as a geometric fundamental group
Gal(Qp/Qp) as a geometric fundamental group
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Gal(Qp/Qp) 作为几何基本群
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发表时间：
2016
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通讯作者：
Jared Weinstein
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文献类型：
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作者：
Jared Weinstein
设p是一个素数。本文给出了Peter Scholze提出的一个定理，即Gal（Qp/Qp）是定义在代数闭域上的某个对象Z的标准基本群。因此，Gal（Qp/Qp）的p-adic表示对应于Z上的Qp-局部系统。精确定理涉及完美空间[Sch 12]。设C/Qp是完备的代数闭的。设D是中心为1的开单位圆盘，D是C上的刚性空间，给出了Zp-模的结构，其中复合律是乘法，a ∈ Zp作用于x7 → xa.设D = lim ←− x 7→xp D。
Let p be a prime number. In this article we present a theorem, suggested by Peter Scholze, which states that Gal(Qp/Qp) is the etale fundamental group of certain object Z which is defined over an algebraically closed field. As a consequence, p-adic representations of Gal(Qp/Qp) correspond to Qp-local systems on Z. The precise theorem involves perfectoid spaces, [Sch12]. Let C/Qp be complete and algebraically closed. Let D be the open unit disk centered at 1, considered as a rigid space over C, and given the structure of a Zp-module where the composition law is multiplication, and a ∈ Zp acts by x 7→ xa. Let D = lim ←− x 7→xp D.