The de Jong fundamental group of a non-trivial abelian variety is non-abelian

2025/12/10 by Sean Howe, Howe, Sean · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Holomorphic and Operator Theory #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2512.09661

openalex publication_date 2025/12/10 · openalex created_date 2025/12/12 · openalex updated_date 2026/07/28

Abstract

We show that the de Jong fundamental group of any non-trivial abelian variety over a complete algebraically closed extension C/ℚ_p is non-abelian. Generalizing an argument for ℙ¹_C, we also show that the de Jong fundamental group of any connected rigid analytic variety over C admitting a non-constant map to ℙⁿ_C (e.g., an abelian variety) depends on C and is big.

Citations

• The de Jong fundamental group of ℙ¹_C depends on C and is not always topologically countably generated
• The geometric Sen morphism is the unique lift of the Kodaira--Spencer morphism
• Characterizing perfectoid covers of abelian varieties
• A Jacquet-Langlands functor for p-adic locally analytic representations
• Geometric Sen theory over rigid analytic spaces
• The six functors for Zariski-constructible sheaves in rigid geometry
• The six functors for Zariski-constructible sheaves in rigid geometry
• Geometrization of the local Langlands correspondence: an overview
• Moduli of p-divisible groups

Cited by

• The de Jong fundamental group of ℙ¹_C depends on C and is not always topologically countably generated

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