TL;DR
This paper introduces a new, unified GAGA theorem that generalizes existing results, applies to non-noetherian settings, and facilitates proofs of Lefschetz and comparison theorems for the Fargues-Fontaine curve.
Contribution
It presents a comprehensive GAGA theorem that unifies and extends previous results, including non-noetherian cases and applications to the Fargues-Fontaine curve.
Findings
Recovers all known analytic and formal GAGA results
Valid in non-noetherian settings
Enables Lefschetz and comparison theorems for Fargues-Fontaine curve
Abstract
We prove a new and unified GAGA theorem. This recovers all analytic and formal GAGA results in the literature, and is also valid in the non-noetherian setting. Our method can also be used to establish various Lefschetz theorems and comparison results for the Fargues-Fontaine curve.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Numerical Analysis Techniques