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Deformation theory of periodic Higgs-de Rham flows

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arxiv 2005.00579 v1 pith:EX6PCBFJ submitted 2020-05-01 math.AG

Raju Krishnamoorthy , Jinbang Yang , Kang Zuo This is my paper · ORCID
classification math.AG
keywords deformationtheorytorsionconditioncrystallineflowshiggs-delogarithmic
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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 $p^n$-torsion crystalline representation to deform to a $p^{n+1}$-torsion crystalline representation.

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  1. Algebraicity and integrality of solutions to differential equations

    math.AG 2025-01 conditional novelty 8.0 of 10

    Solutions of algebraic differential equations are conjectured to be algebraic exactly when their Taylor coefficients have almost no primes in their denominators, and the conjecture is proved for Picard-Fuchs equations...

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