Semistable Modules over Lie Algebroids in Positive Characteristic

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.

2010 Mathematics Subject Classification: 14D20, 14G17, 17B99

Keywords and Phrases: Lie algebroids, Langton's theorem, sheaves with connection, Higgs sheaves, positive characteristic

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