Surjectivity and flatness over DVR's (after Moret-Bailly)

2025/06/02 by Benedictus Margaux, Margaux, Benedictus
Mathematics · #14B25 #14E22 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2506.01313

openalex publication_date 2025/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study morphisms of schemes f : X → S which are locally of finite type. We present conditions under which there exists a morphism g : S'→ X of S--schemes such that f ∘ g is the canonical morphism S'→ S. Furthermore, we exhibit situations in which f is flat surjective. Our results are mostly concerned with S being the spectrum of a DVR.

Citations

• Isotopes of Octonion Algebras, G2-Torsors and Triality
• The p-radical closure of local noetherian rings

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