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arXiv · 2202.02657

Notes on the Twistor $\mathbf P^1$

Peter Woit
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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.

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Peter Woit. 2022-02-05. Notes on the Twistor $\mathbf P^1$. https://arxiv.org/abs/2202.02657

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