Scholze's diamond
Overview
The diamond functor from p-adic spaces to v-sheaves. Scholze (2014–) developed it for the Fargues–Fontaine curve and the local Langlands program. Replaces rigid geometry in many settings.
Era: 2014–
Proposed at: Bonn, Germany
Formal structure
Domain: Adic space X; pro-étale site X_proét
X^⋄ = (X / ≈) as v-sheaf; X^⋄ = Spd(R,R^+) for affinoid
Constraints: v-sheaf: sheaf on v-site (perfectoid spaces); functorial
Objective: Fargues–Fontaine curve; local Langlands; shtukas