Direct summand conjecture and perfectoid Abhyankar lemma: an overview

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

mercredi 2 nov. 2016, 10:00 → 11:00 Europe/Paris

Centre de conférences Marilyn et James Simons (IHES)

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.