A note on Diophantine subsets of large fields

Andrew Kwon

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arXiv · 2411.03212

A note on Diophantine subsets of large fields

Andrew Kwon

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Abstract

Large fields (also called ample, anti-mordellic) generalize many fields of classical interest, such as algebraically closed fields, real-closed fields, and $p$-adic fields. In this note we answer a question of Pop by generalizing a result of Fehm and prove that finite unions of affine translates of infinite proper subfields are never diophantine subsets of perfect large fields.

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Andrew Kwon. 2024-11-05. A note on Diophantine subsets of large fields. https://arxiv.org/abs/2411.03212

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