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arXiv · 2304.09266

A Berkovich Approach to Perfectoid Spaces

Attilio Castano
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Abstract

Since their inception perfectoid spaces have catalyzed a revolution in p-adic geometry. We redevelop the foundations of perfectoid spaces from the point of view of Berkovich Spaces, where the underlying topological space of an affinoid perfectoid space is a compact Hausdorff space -- closely resembling the situation in complex geometry. The key technical ingredient in our construction is arc_pi-descent for perfectoid Banach algebras. Along the way, we establish various foundational results for arc_pi-sheaves, notably a form of the Gerritzen-Grauert theorem.

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Attilio Castano. 2023-04-18. A Berkovich Approach to Perfectoid Spaces. https://arxiv.org/abs/2304.09266

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