Indexed on: 11 Jul '14Published on: 11 Jul '14Published in: Inventiones mathematicae
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.