Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo

Direct summand conjecture and perfectoid Abhyankar lemma: an overview

par Prof. Y. ANDRÉ (CNRS, Institut de Mathématiques de Jussieu)

Europe/Paris
Centre de conférences Marilyn et James Simons (IHES)

Centre de conférences Marilyn et James Simons

IHES

Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description

According to Hochster's direct summand conjecture (1973), a regular ring R is a direct summand, as an R-module, of every finite extension ring. We shall outline our recent proof which relies on perfectoid techniques. Similar arguments also establish the existence of big Cohen-Macaulay algebras for complete local domains of mixed characteristics.

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