On the rationality and continuity of logarithmic growth filtration of solutions of $p$-adic differential equations

Shun Ohkubo

doi:10.1016/j.aim.2016.12.006

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arXiv · 1502.03804

On the rationality and continuity of logarithmic growth filtration of solutions of $p$-adic differential equations

Shun Ohkubo

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Abstract

We study the asymptotic behavior of solutions of Frobenius equations defined over the ring of overconvergent series. As an application, we prove Chiarellotto-Tsuzuki's conjecture on the rationality and right continuity of Dwork's logarithmic growth filtrations associated to ordinary linear $p$-adic differential equations with Frobenius structures.

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Shun Ohkubo. 2015-02-12. On the rationality and continuity of logarithmic growth filtration of solutions of $p$-adic differential equations. https://doi.org/10.1016/j.aim.2016.12.006

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