Logarithmic nonabelian Hodge theory in characteristic p

Details Logarithmic nonabelian Hodge theory in characteristic p Logarithmic nonabelian Hodge theory in characteristic p

2008-02-14

arxiv.org/abs/0802.1977v1

Mathematics

Algebraic Geometry

Scientific paper

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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