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Bootstrapping GAGA Theorems

Primarily human-written textHuman understanding: all partsmath.AG — Algebraic Geometry

Contributed by Aniruddh Venkatesan ↗

Version 1 / Nov 12, 2026 / CC BY 4.0

Abstract

Let XX be a noetherian scheme with affine diagonal, and let λ:X→X\lambda : \mathcal{X} \to X be a morphism of locally ringed spaces from a qcqs locally strongly noetherian analytic adic space. We prove that an equivalence on coherent sheaves, together with comparison of their cohomology, extends to every proper XX-scheme. As an application, we obtain GAGA for proper schemes over the Fargues--Fontaine curve in equal and mixed characteristic.

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Version history

  1. v1 · 72 pagesSubmitted by Aniruddh VenkatesanInitial depositCurrentNov 12, 2026