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Logarithmic growth filtrations for
$(\varphi ,\nabla )$-modules over the bounded Robba ring
Published online by Cambridge University Press: 04 June 2021
Abstract
In the 1970s, Dwork defined the logarithmic growth (log-growth for short) filtrations for $p$-adic differential equations
$Dx=0$ on the
$p$-adic open unit disc
$|t|<1$, which measure the asymptotic behavior of solutions
$x$ as
$|t|\to 1^{-}$. Then, Dwork calculated the log-growth filtration for
$p$-adic Gaussian hypergeometric differential equation. In the late 2000s, Chiarellotto and Tsuzuki proposed a fundamental conjecture on the log-growth filtrations for
$(\varphi ,\nabla )$-modules over
$K[\![t]\!]_0$, which can be regarded as a generalization of Dwork's calculation. In this paper, we prove a generalization of the conjecture to
$(\varphi ,\nabla )$-modules over the bounded Robba ring. As an application, we prove a generalization of Dwork's conjecture proposed by Chiarellotto and Tsuzuki on the specialization property for log-growth Newton polygons.
MSC classification
- Type
- Research Article
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- Copyright
- © The Author(s) 2021
References
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