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Creators/Authors contains: "Dorfsman-Hopkins, Gabriel"

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  1. ; ; (, European Journal of Mathematics)
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  2. (, International Mathematics Research Notices)
    Abstract Let $$X$$ be a perfectoid space with tilt $$X^\flat $$. We build a natural map $$\theta :\Pic X^\flat \to \lim \Pic X$$ where the (inverse) limit is taken over the $$p$$-power map and show that $$\theta $$ is an isomorphism if $$R = \Gamma (X,\sO _X)$$ is a perfectoid ring. As a consequence, we obtain a characterization of when the Picard groups of $$X$$ and $$X^\flat $$ agree in terms of the $$p$$-divisibility of $$\Pic X$$. The main technical ingredient is the vanishing of higher derived limits of the unit group $R^*$, whence the main result follows from the Grothendieck spectral sequence. 
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