
doi: 10.1093/imrn/rnw072
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.
| 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). | 1 | |
| 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. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
