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Monodromy representations of $p$-adic differential equations in families
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abstract
We derive a relative version of the local monodromy theorem for ordinary differential equations on an annulus over a mixed-characteristic nonarchimedean field, and give several applications in $p$-adic cohomology and $p$-adic Hodge theory. These include a simplified proof of the semistable reduction theorem for overconvergent $F$-isocrystals, a relative version of Berger's theorem that de Rham representations are potentially semistable, and a multivariate version of the local monodromy theorem in the style of Drinfeld's lemma on fundamental groups.
Forward citations
Cited by 2 Pith papers
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Compatibility of $F$-isocrystals on adjoint Shimura varieties
For adjoint Shimura varieties in the superrigid regime, the canonical overconvergent F-isocrystal has Frobenius conjugacy classes with rational, ℓ-independent characteristic polynomials matching the canonical ℓ-adic l...
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On generalized Fuchs theorem over relative $p$-adic polyannuli
The paper proves new splitting theorems for p-adic differential modules over relative polyannuli and shows that the Christol-Mebkhout and Dwork definitions of p-adic exponents coincide.
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