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Preprint Number 1839

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1839. Will Johnson, Chieu-Minh Tran, Erik Walsberg, Jinhe Ye
Etale-open topology and the stable field conjecture

Submission date: 4 September 2020


Preliminary version, comments are welcome

For an arbitrary field K and K-variety V, we introduce the étale-open topology on the set V(K) of K-points of V. This topology agrees with the Zariski topology, Euclidean topology, valuation topology when K is separably closed, real closed, p-adically closed, respectively. The étale open topology on 𝔸^1(K) is not discrete if and only if K is large. Topological properties of the étale open topology corresponds to algebraic properties of K. As an application, we show that a large stable field is separably closed.

Mathematics Subject Classification: 03C60, 14G27, 12E30

Keywords and phrases:

Full text arXiv 2009.02319: pdf, ps.

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