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

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.

26 pages; v3: refereed version, to appear in Advances in Mathematics

References in corpus (1)

• Slope filtrations revisited