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arXiv · 2108.01868

The \'etale open topology over the fraction field of a henselian local domain

Will Johnson·Erik Walsberg·Jinhe Ye
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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 \'etale open topology. If $R$ is regular then the \'etale open topology over $K$ refines the $R$-adic topology. In particular the \'etale open topology over $L((t_1,\ldots,t_n))$ agrees with the $L[[t_1,\ldots,t_n]]$-adic topology for any field $L$ and $n \ge 1$.

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Will Johnson, Erik Walsberg, Jinhe Ye. 2021-08-04. The \'etale open topology over the fraction field of a henselian local domain. https://doi.org/10.1002/mana.202100418

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