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Let $R$ be a Noetherian local ring and let $R^h$ be its Henselization. What can we say about the kernel and range of the map $$ \operatorname{Br}(R) \rightarrow \operatorname{Br}(R^h)? $$ Are there interesting situations when the map is injective? Do we know more when $R$ is a discrete valuation ring?

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    $\begingroup$ commenting just to link a related question I asked (still haven't worked out Piotr's suggestion) $\endgroup$
    – Minseon Shin
    Jan 6, 2021 at 20:19
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    $\begingroup$ @‍PiotrAchinger's suggestion on @MinseonShin's question referenced above. $\endgroup$
    – LSpice
    Jan 7, 2021 at 0:16
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    $\begingroup$ Have you tried looking in this book? wwwf.imperial.ac.uk/~anskor/brauer.pdf $\endgroup$
    – Daniel Loughran
    Jan 7, 2021 at 9:22
  • $\begingroup$ @Daniel Loughran: Looked at it superficially but could not find much. Will look deeper. $\endgroup$
    – user123
    Jan 7, 2021 at 17:47

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