Bogomolov’s inequality for Higgs sheaves in positive characteristic. (English) Zbl 1348.14048
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 A. Ogus and 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.
Reviewer: Gerd Faltings (Bonn)
MSC:
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
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