Bogomolov’s inequality for Higgs sheaves in positive characteristic
By A. Langer. 2015
67 citations recorded by the source corpus.
We prove Bogomolov’s inequality for Higgs sheaves on varieties in positive characteristic $$p$$p that can be lifted modulo $$p^2$$p2. This implies the Miyaoka–Yau inequality on surfaces of non-negative Kodaira dimension liftable modulo $$p^2$$p2. 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0a5e1fc87d63d029f041cc84f2480e1001275aab
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Semistable Higgs bundles, periodic Higgs bundles and representations of algebraic fundamental groups (2013, background): “Langer [20], on the Bogomolov-Gieseker inequality for semistable Higgs bundles and Miyaoka-Yau inequality for surfaces in positive characteristic.”
- The Miyaoka-Yau inequality and uniformisation of canonical models (2015, background): “He recently also gave the first purely algebraic proof of the Bogomolov Inequality for semistable Higgs sheaves (on smooth projective varieties over fields of arbitrary characteristic), see [Lan15].”
- Semistable modules over Lie algebroids in positive characteristic (2013, methodology): “t Simpson’s inductive construction must finish. They also obtain a slightly we aker result proving their conjecture only for an algebraic closure of a finite field. The results of this paper are used in [La3] to prove Bogomolov’s type inequality for Higgs sheaves on varieties liftable modulo p2. 0.1 No”