Logarithmic nonabelian Hodge theory in characteristic p

Abstract

Given a morphism $X\to S$ of log schemes of characteristic $p>0$ and a lifting of $X^{\prime }$ 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.

References in corpus (1)

• Nonabelian Hodge Theory in Characteristic p

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• Canonical Heights on Shimura Varieties and the André-Oort Conjecture
• Parabolic log convergent isocrystals
• Intersection de Rham complexes in positive characteristic
• Uniformization of $p$-adic curves via Higgs-de Rham flows
• A note on the filtered decomposition theorem
• On log local Cartier transform of higher level in characteristic $p$