Year: 2022
Type: preprint
Abstract: Remarkably, the twistor $\mathbf P^1$ occurs as a fundamental object in both four-dimensional space-time geometry and in number theory. In Euclidean signature twistor theory it is how one describes space-time points. In recent work by Fargues and Scholze on the local Langlands conjecture using geometric Langlands on the Fargues-Fontaine curve, the twistor $\mathbf P^1$ appears as the analog of this curve at the infinite prime. These notes are purely expository, written with the goal of explaining, in a form accessible to both mathematicians and physicists, various different ways in which the twistor $\mathbf P^1$ makes an appearance, often as a geometric avatar of the quaternions.
Source: arXiv (Cornell University)
Author: Woit, Peter
Institution: Columbia University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4226075855