
Notes on Generalizations of Local OgusVologodsky CorrespondenceNotes on Generalizations of Local OgusVologodsky CorrespondenceAA11021653 
"/Shiho, Atsushi/"Shiho, Atsushi
22
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3
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20150715 , Graduate School of Mathematical Sciences, The University of Tokyo , Graduate School of Mathematical Sciences, University of Tokyo
ISSN:13405705
NCID:AA11021653
Description
Given a smooth scheme over Z/pnZ with a lift of relative Frobenius to Z/pn+1Z, we construct a functor from the category of Higgs modules to that of modules with integrable connection as the composite of the level raising inverse image functors from the category of modules with integrable pmconnection to that of modules with integrable pm−1connection for 1 ≤ m ≤ n. In the case m = 1, we prove that the level raising inverse image functor is an equivalence when restricted to quasinilpotent objects, which generalizes a local result of OgusVologodsky. We also prove that the above level raising inverse image functor for a smooth padic formal scheme induces an equivalence of Qlinearized categories for general m when restricted to nilpotent objects (in strong sense), under a strong condition on Frobenius lift. We also prove a similar result for the category of modules with integrable pmWittconnection.
FullText
http://repository.dl.itc.utokyo.ac.jp/dspace/bitstream/2261/59549/1/jms220306.pdf