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Le lemme d’Abhyankar perfectoide

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Résumé

Nous étendons le théorème de presque-pureté de Faltings-Scholze-Kedlaya-Liu sur les extensions étales finies d’algèbres perfectoïdes au cas des extensions ramifiées, sans restriction sur le lieu de ramification. Nous déduisons cette version perfectoïde du lemme d’Abhyankar du théorème de presque-pureté, par un passage à la limite mettant en jeu des versions perfectoïdes du théorème d’extension de Riemann. Au préalable, nous développons les aspects catégoriques des algèbres de Banach uniformes et des algèbres perfectoïdes, tout en semant de nouvelles notions (algèbres presque perfectoïdes) et techniques galoisiennes.

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  1. Institut de Mathématiques de Jussieu, 4 place Jussieu, 75005, Paris, France

    Yves André

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  1. Yves André
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Correspondence to Yves André.

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André, Y. Le lemme d’Abhyankar perfectoide. Publ.math.IHES 127, 1–70 (2018). https://doi.org/10.1007/s10240-017-0096-x

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