On logarithmic nonabelian Hodge theory of higher level in characteristic p

2014/01/15 by Ohkawa, Sachio
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1401.3574

Abstract

Given a natural number m and a log smooth integral morphism X→ S of fine log schemes of characteristic p>0 with a lifting of its Frobenius pull-back X'→ S modulo p², we use indexed algebras \cal A_X^gp, \cal B_X/S^(m+1) of Lorenzon-Montagnon and the sheaf \cal D_X/S^(m) of log differential operators of level m of Berthelot-Montagnon to construct an equivalence between the category of certain indexed \cal A_X^gp-modules with \cal D_X/S^(m)-action and the category of certain indexed \cal B_X/S^(m+1)-modules with Higgs field. Our result is regarded as a level m version of some results of Ogus-Vologodsky and Schepler.

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