Characteristic-free Resolution of Singularity
Prof. Yi Hu
2025-07-01 10:30-11:30
MCM110
Speaker: Prof. Yi Hu (The University of Arizona)
Time: 10:30-11:30 July 1st, 2025 (Tuesday)
Venue: MCM110
Title: Characteristic-free Resolution of Singularity
Abstract: We prove the following Theorem. Let X be any affine singular variety defined over the integers Z. Then there exist morphisms Y→ X' → X such that: X'→ X is a smooth morphism, Y is smooth and Y→ X' is surjective, proper, and birational.
In other words, X admits a resolution of singularities up to smooth morphism. Our method is characteristic-free. This constitutes the first result of such kind, regardless of characteristics, ever since Hironaka's Fields medal work over characteristic zero in 1964.
In this talk, I will explain the existence of X' (which was previously known) and the existence of Y, which is our contribution. Our approach is fundamentally distinct from Hironaka's, hence also differs in technique from all subsequent works that in essence follow Hironaka's.
