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Vector Bundles on Perfectoid Spaces

Abstract

We explicitly compute the Picard groups of the projectivoid line and its corresponding characteristic $p$ tilt. The desire to generalize this to higher-dimensional projectivoid spaces, as well as other perfectoid spaces, leads us to ask whether a GAGA principle holds between perfections of analytifiable schemes in characteristic $p$, and corresponding completed perfections of their adic analytifications.

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