Abstract:In this paper, we study the logarithmic growth (log-growth) filtration, a mysterious invariant found by B. Dwork, for (ϕ, ∇)-modules over the bounded Robba ring. The main result is a proof of a conjecture proposed by B. Chiarellotto and N. Tsuzuki on a comparison between the log-growth filtration and Frobenius slope filtration. One of the ingredients of the proof is a new criterion for pure of bounded quotient, which is a notion introduced by Chiarellotto and Tsuzuki to formulate their conjecture. We also give… Show more
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