Macaulayfication of Noetherian schemes

Kęstutis Česnavičius, Université Pari-Sud/MSRI
IAS - Simonyi Hall Seminar Room SH-101

To reduce to resolving Cohen–Macaulay singularities, Faltings initiated the program of "Macaulayfying" a given Noetherian scheme X. Under various assumptions Faltings, Brodmann, and Kawasaki built the sought Cohen–Macaulay modifications without preserving the locus where X is already Cohen–Macaulay. We will discuss an approach that overcomes this difficulty and hence completes Faltings' program.