Logarithmic nonabelian Hodge theory in characteristic p

2008/02/14 by Daniel Schepler, Schepler, Daniel
Mathematics · #14A20 #14F30 #14F40 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14A20 #msc:14F30 #msc:14F40

paper · pdf · doi:10.48550/arxiv.0802.1977

arxiv created 2008/02/14 · arxiv updated 2009/12/01

Abstract

Given a morphism X → S of log schemes of characteristic p > 0 and a lifting of X' over S modulo p², 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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