Semistable modules over Lie algebroids in positive characteristic

Abstract

We study Lie algebroids in positive characteristic and moduli spaces of their modules. In particular, we show a Langton's type theorem for the corresponding moduli spaces. We relate Langton's construction to Simpson's construction of gr-semistable Griffiths transverse filtration. We use it to prove a recent conjecture of Lan-Sheng-Zuo that semistable systems of Hodge sheaves on liftable varieties in positive characteristic are strongly semistable.

v2: changed formatting, 30 pages, corrections in 4.2, 5.1 and 5.2, to appear in Documenta Mathematica

References in corpus (4)

• Localization of modules for a semisimple Lie algebra in prime characteristic
• Semistable Higgs bundles and representations of algebraic fundamental groups: Positive characteristic case
• Semistable Higgs bundles of small ranks are strongly Higgs semistable
• On a Conjecture of Lan-Sheng-Zuo on Semistable Higgs Bundles: Rank 3 Case

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• Canonical Heights on Shimura Varieties and the André-Oort Conjecture
• A Lefschetz theorem for crystalline representations
• Moduli of rank 1 isocrystals
• Twisted functoriality in nonabelian Hodge theory in positive characteristic
• Finiteness of logarithmic crystalline representations II
• On the Bogomolov-Gieseker inequality for tame Deligne-Mumford surfaces
• Moduli spaces of semistable modules over Lie algebroids
• Tensor product theorem for parabolic $\lambda$-connections
• A Simpson correspondence for abelian varieties in characteristic p > 0