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International Mathematics Research Notices
Article . 2016 . Peer-reviewed
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Gal(Qp/Qp) as a geometric fundamental group

Authors: Jared Weinstein;

Gal(Qp/Qp) as a geometric fundamental group

Abstract

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.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
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