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Publications mathématiques de l'IHÉS

, Volume 127, Issue 1, pp 1–70 | Cite as

Le lemme d’Abhyankar perfectoide

Article

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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Copyright information

© IHES and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Institut de Mathématiques de JussieuParisFrance

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