Bogomolov's inequality for Higgs sheaves in positive characteristic
type: Item
instance of: scholarly article
title: Bogomolov's inequality for Higgs sheaves in positive characteristic
zbMATH Open document ID: 1348.14048
author: Adrian Langer
published in: Inventiones Mathematicae
publication date: 2015-03-23T00:00:00Z
review text: The paper under review deals with bundles in positive characteristic and extends results previously only known in characteristic zero. The main assumption is that the variety extends to the Witt vectors of length two. This allows to use the results of \textit{A. Ogus} and \textit{V. Vologodsky} [Publ. Math., Inst. Hautes Étud. Sci. 106, 1--138 (2007; Zbl 1140.14007)]. In addition an important technical tool is the author's previous result [Doc. Math., J. DMV 19, 509--540 (2014; Zbl 1330.14017)] constructing a good filtration (satisfying Griffiths' transversality) on semistable crystals. The main results are Bogomolov's inequality for stable Higgs sheaves of rank \(\leq p\), various restriction theorems (the restriction of a semistable Higgs to a hypersurface is semistable) and local freeness of semistable Higgs with vanishing first two Chern classes.
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 6418046
zbMATH Keywords: Higgs bundles
zbMATH Keywords: semistability
MaRDI profile type: Publication
full work available at URL: s00222-014-0534-z
OpenAlex ID: W2012864822
Wikidata QID: Q59406073
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DOI: 10.1007/S00222-014-0534-Z
reviewed by: Gerd Faltings
description: scientific article; zbMATH DE number 6418046