On logarithmic nonabelian Hodge theory of higher level in characteristic pp

  • Sachio Ohkawa

    University of Tokyo, Japan

Abstract

Given a natural number mm and a log smooth integral morphism XSX\to S of fine log schemes of characteristic p>0p>0 with a lifting of its Frobenius pull-back XSX'\to S modulo p2p^{2}, we use indexed algebras AXgp{\mathcal A}_{X}^{gp}, BX/S(m+1){\mathcal B}_{X/S}^{(m+1)} of Lorenzon-Montagnon and the sheaf DX/S(m){\cal D}_{X/S}^{(m)} of log differential operators of level mm of Berthelot-Montagnon to construct an equivalence between the category of certain indexed AXgp{\mathcal A}^{gp}_{X}-modules with DX/S(m){\mathcal D}_{X/S}^{(m)}-action and the category of certain indexed BX/S(m+1){\mathcal B}_{X/S}^{(m+1)}-modules with Higgs field. Our result is regarded as a level mm version of some results of Ogus-Vologodsky and Schepler.

Cite this article

Sachio Ohkawa, On logarithmic nonabelian Hodge theory of higher level in characteristic pp. Rend. Sem. Mat. Univ. Padova 134 (2015), pp. 47–91

DOI 10.4171/RSMUP/134-2