The étale open topology over the fraction field of a henselian local domain

Abstract

Suppose that $R$ is a local domain with fraction field $K$. If $R$ is Henselian then the $R$-adic topology over $K$ refines the étale open topology. If $R$ is regular then the étale open topology over $K$ refines the $R$-adic topology. In particular the étale open topology over $L((t_1,\dots ,t_n))$ agrees with the $L[[t_1,\dots ,t_n]]$-adic topology for any field $L$ and $n\ge 1$.

References in corpus (1)

• Éz fields

Cited by in corpus (2)

• Hyperbolicity and model-complete fields
• When is the étale open topology a field topology?