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

In his study of p-adic differential equations, B.Dwork proved that the power series solutions of certain p-adic differential equations such as (p-adic) Gaussian hypergeometric one satisfy a mild growth condition. Recently, B.Chiarellotto and N.Tsuzuki reconsidered Dwork's work and conjectured a relationship between the order of growth and Frobenius slopes of the space of solutions. In this talk, we discuss some part of Chiarellotto-Tsuzuki conjecture.