Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo

Direct summand conjecture and perfectoid Abhyankar lemma: an overview

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

Centre de conférences Marilyn et James Simons (IHES)

Centre de conférences Marilyn et James Simons


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

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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