Direct summand conjecture and perfectoid Abhyankar lemma: an overview
By Yves André
Appears in collection : Conférences Paris Pékin Tokyo
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.
