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Deformation theory of periodic Higgs-de Rham flows (2005.00579v1)
Published 1 May 2020 in math.AG
Abstract: In this note we study the deformation theory of periodic (logarithmic) Higgs-de Rham flows. Under suitable numerical assumptions, this is equivalent to the deformation theory of torsion (logarithmic) Fontaine-Faltings modules. As an application, we formulate an \emph{ordinarity} condition, which provides a sufficient condition for a $pn$-torsion crystalline representation to deform to a $p{n+1}$-torsion crystalline representation.
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