Le lemme d'Abhyankar perfectoide

2016/08/31 by Andre, Yves · 1 citation
#11S15 #14G20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.00320

Abstract

We extend Faltings's "almost purity theorem" on finite etale extensions of perfectoid algebras (as generalized by Scholze and Kedlaya-Liu) to the ramified case, without restriction on the discriminant. The key point is a perfectoid version of Riemann's extension theorem. Categorical aspects of uniform Banach algebras and perfectoid algebras are revisited beforehand.

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• δ-rings, perfectoid towers, and lim Cohen-Macaulay sequences

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