Existence of an exact tensor functor from étale Q_p-local systems to p-adic twistor structures

Develop an exact tensor functor that assigns to each étale \mathbb{Q}_p-local system on a smooth rigid analytic variety Z a corresponding p-adic variation of twistor structures over Z, with compatibility under tensor operations, as conjectured by Fargues and Liu–Zhu.

Background

The paper constructs a fully faithful exact tensor functor Tw from étale \mathbb{Q}_p-local systems on Z to twistor bundles on the relative thickened Fargues–Fontaine curve over Z^{\wedge}, realizing a form of a twistor correspondence in the inscribed (thickened) setting.

The authors note that Fargues and Liu–Zhu previously conjectured the existence of such an exact tensor functor from local systems to p-adic twistor structures over Z. While the present construction provides a precise inscribed version, the authors remark that it may differ from the exact formulation envisioned by Fargues and Liu–Zhu, so the broader conjectural program remains open.