ﻻ يوجد ملخص باللغة العربية
We study Lie algebroids in positive characteristic and moduli spaces of their modules. In particular, we show a Langtons type theorem for the corresponding moduli spaces. We relate Langtons construction to Simpsons 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.
We show a few basic results about moduli spaces of semistable modules over Lie algebroids. The first result shows that such moduli spaces exist for relative projective morphisms of noetherian schemes, removing some earlier constraints. The second res
We study geometric representation theory of Lie algebroids. A new equivalence relation for integrable Lie algebroids is introduced and investigated. It is shown that two equivalent Lie algebroids have equivalent categories of infinitesimal actions of
We construct a family of homomorphisms between Weyl modules for affine Lie algebras in characteristic p, which supports our conjecture on the strong linkage principle in this context. We also exhibit a large class of reducible Weyl modules beyond level one, for p not necessarily small.
Let $G$ be a reductive group, and let $X$ be an algebraic curve over an algebraically closed field $k$ with positive characteristic. We prove a version of nonabelian Hodge correspondence for $G$-local systems over $X$ and $G$-Higgs bundles over the F
We study the existence of Fuchsian differential equations in positive characteristic with nilpotent p-curvature, and given local invariants. In the case of differential equations with logarithmic local mononodromy, we determine the minimal possible degree of a polynomial solution.