Largeness and generalized t-henselianity

2025/08/21 by Johnson, Will · 1 citation
#12E30 #12J99 #12L12 #Commutative Algebra (math.AC) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2508.15362

Abstract

Let K be a countable field. Then K is large in the sense of Pop if and only if it admits a field topology which is "generalized t-henselian" (gt-henselian) in the sense of Dittmann, Walsberg, and Ye, meaning that the implicit function theorem holds for polynomials. Moreover, the étale open topology can be characterized in terms of the gt-henselian topologies on K: a subset U ⊆ Kⁿ is open in the étale open topology if and only if it is open with respect to every gt-henselian topology on K.

Citations

• Large implies henselian
• Translating between NIP integral domains and topological fields
• When is the étale open topology a field topology?

Cited by

• Derivations and gt-henselian field topologies

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