A conjecture of Ax and degenerations of Fano varieties

2005/12/15 by Janós Kollár, János Kollár, Kollár, János
Mathematics · #12E30 14J45 (primary) 11U05 14G27 (secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #math.AG #math.NT #msc:11U05 #msc:12E30 #msc:14G27 #msc:14J45

paper · pdf · doi:10.48550/arxiv.math/0512375

arxiv created 2005/12/15 · openalex publication_date 2005/12/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

James Ax conjectured that every pseudo algebraically closed field is C₁. We prove this conjecture in characteristic 0 by relating it to degenerations of Fano varieties.

Related

• Degenerations of rationally connected varieties and PAC fields
• On rationally connected varieties over C₁ fields of characteristic 0
• The pseudo-index of horospherical Fano varieties
• A vanishing theorem for Fano varieties in positive characteristic
• Fano varieties with conjecturally largest Fano index