Speaker:
Adrian Langer
Title:
Bogomolov's inequality for Higgs sheaves in positive characteristic
Abstract:
We prove Bogomolov's inequality for Higgs sheaves on varieties
in positive characteristic $p$ that can be lifted modulo $p^2$.
This implies the Miyaoka–Yau inequality on surfaces of
non-negative Kodaira dimension liftable modulo $p^2$.
This result is a strong version of Shepherd-Barron’s conjecture.
Our inequality also gives the first algebraic proof of Bogomolov's
inequality for Higgs sheaves in characteristic zero,
solving the problem posed by Narasimhan.
