Stone duality between condensed mathematics and algebraic geometry

2024/01/04 by Rok Gregoric, Gregoric, Rok · 1 citation
Mathematics · #14A20 #18F70 #54B30 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.2401.02568

openalex publication_date 2024/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend Stone duality to a fully faithful embedding of condensed sets into fpqc sheaves over an arbitrary field, which preserves colimits and finite limits. We study how familiar notions from condensed mathematics/topology and algebraic geometry correspond to each other under this form of Stone duality.

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