Another proof of the almost purity theorem for perfectoid valuation rings
arXiv:2012.13984 · doi:10.1016/j.jpaa.2021.106898
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.
to appear in J. of Pure and Applied Algebra