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

Will Johnson, Erik Walsberg and Jinhe Ye

Mathematische Nachrichten, 2023, vol. 296, issue 5, 1928-1937

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((t1,…,tn))$L((t_1,\ldots ,t_n))$ agrees with the L[[t1,…,tn]]$L[[t_1,\ldots ,t_n]]$‐adic topology for any field L and n≥1$n \ge 1$.

Date: 2023
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https://doi.org/10.1002/mana.202100418

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