There is an equivalence of 2-categories of G-gerbes on the v-site and étale site of a perfectoid space X over a complete non-archimedean field K.
[SW20] Peter Scholze and Jared Weinstein,Berkeley lectures onp-adic geometry, Annals of Math- ematics Studies, vol
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$G$-gerbes on perfectoid spaces
There is an equivalence of 2-categories of G-gerbes on the v-site and étale site of a perfectoid space X over a complete non-archimedean field K.