A parabolic-bases framework is used to construct the parabolic non-abelian Hodge correspondence in positive characteristic on arbitrary-dimensional log varieties, extending Krishnamoorthy-Sheng's curve-level result.
Logarithmic nonabelian Hodge theory in characteristic p
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Given a morphism $X \to S$ of log schemes of characteristic $p > 0$ and a lifting of $X'$ over $S$ modulo $p^2$, we use Lorenzon's indexed algebras $A_X^{gp}$ and $B_{X/S}$ to construct an equivalence between $O_X$-modules with nilpotent integrable connection and indexed $B_{X/S}$-modules with nilpotent $B_{X/S}$-linear Higgs field. If either satisfies a stricter nilpotence condition, we find an isomorphism between the de Rham cohomology of the connection and the Higgs cohomology of the Higgs field.
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Constructing Parabolic Non-Abelian Hodge Correspondence in Positive Characteristic Using Parabolic Bases
A parabolic-bases framework is used to construct the parabolic non-abelian Hodge correspondence in positive characteristic on arbitrary-dimensional log varieties, extending Krishnamoorthy-Sheng's curve-level result.