Submission date: 4 September 2020

Abstract:

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.