Another proof of the almost purity theorem for perfectoid valuation rings

Shinnosuke Ishiro; Kazuma Shimomoto

doi:10.1016/j.jpaa.2021.106898

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arXiv · 2012.13984

Another proof of the almost purity theorem for perfectoid valuation rings

Shinnosuke Ishiro·Kazuma Shimomoto

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Abstract

The almost purity theorem is central to the geometry of perfectoid spaces and has numerous applications in algebra and geometry. This result is known to have several different proofs in the case that the base ring is a perfectoid valuation ring. We give a new proof by exploiting the behavior of Faltings' normalized length under the Frobenius map.

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BibTeX RIS

Shinnosuke Ishiro, Kazuma Shimomoto. 2020-12-27. Another proof of the almost purity theorem for perfectoid valuation rings. https://doi.org/10.1016/j.jpaa.2021.106898

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