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.
Last modified on: 26-Nov-14