Derivations and gt-henselian field topologies

2025/09/02 by Erik Walsberg, Walsberg, Erik
Mathematics · #Advanced Topology and Set Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2509.02889

openalex publication_date 2025/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that K is a characteristic zero field with infinite transcendence degree over its prime subfield. We show that if there is a gt-henselian topology on K then there are 2^2^|K| pairwise incomparable gt-henselian topologies on K. It follows by applying a recent theorem of Will Johnson that if K is large and countable then there are 2^2^ℵ₀ pairwise incomparable gt-henselian topologies on K. We also formulate several conjectures concerning gt-henselian field topologies and their relationship with the étale-open topology.

Citations

• Largeness and generalized t-henselianity
• Large implies henselian
• Curve-excluding fields
• When is the étale open topology a field topology?
• Topological proofs of results on large fields
• Open Problems in the Theory of Ample Fields

Related

• Largeness and generalized t-henselianity
• Definable V-topologies, Henselianity and NIP
• Large implies henselian
• Uniformly defining p-henselian valuations
• When is the étale open topology a field topology?