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

Ohkubo, Shun

doi:10.1016/j.aim.2016.12.006

Cited by 5 publications

(13 citation statements)

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“…Chiarellotto and Tsuzuki proved the conjecture in the rank case [CT09, Theorem 7.1(1)]. The present author proved part (i) of the conjecture without assumptions [Ohk17, Theorem 3.7(i)].…”

Section: Introductionmentioning

confidence: 69%

“…Lemma 3.9 (Cf. [Ohk17,Theorem 6.1]). If g ∈R log is a d-eigenvector of slope λ (Definition 2.9), then we have λ 0, and g has exact log-growth λ.…”

Section: Technical Resultsmentioning

confidence: 99%

“…First proof of part (i) of Theorem 0.1. By Remark 5.2, we may assume that X = t, in which case the assertion is nothing but [Ohk17,Theorem 4.19].…”

Section: Logarithmic Growth Filtrations For (ϕ ∇)-Modules Over R Bdmentioning

confidence: 99%

“…We define the log-growth filtration of K{t} log by Fil λ K{t} log := K{t} log ∩ Fil λ R log for λ ∈ R (cf. [Ohk17,Definition 4.11]). By using the claim, we can define V (M ), Sol(M ), etc., for log-(ϕ, ∇)-modules M over K [[t]] 0 as in § 5.…”

Section: Then Condition (I) Implies Condition (Ii) Moreover If K Is Perfect Then Condition (Ii) Implies Condition (I)mentioning

confidence: 99%

“…We prove part (ii) of Theorem 0.1 in § 8. We give two proofs of part (i) of Theorem 0.1; the first given in § 5 is done by a reduction to the case , in which case the assertion is proved in [Ohk17, Theorem 4.19], and the second given in § 10 is simple and self-contained.…”

Section: Introductionmentioning

confidence: 99%

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Logarithmic growth filtrations for -modules over the bounded Robba ring

Ohkubo¹

2021

Compositio Math.

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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.

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“…Chiarellotto and Tsuzuki proved the conjecture in the rank case [CT09, Theorem 7.1(1)]. The present author proved part (i) of the conjecture without assumptions [Ohk17, Theorem 3.7(i)].…”

Section: Introductionmentioning

confidence: 69%

“…Lemma 3.9 (Cf. [Ohk17,Theorem 6.1]). If g ∈R log is a d-eigenvector of slope λ (Definition 2.9), then we have λ 0, and g has exact log-growth λ.…”

Section: Technical Resultsmentioning

confidence: 99%

“…First proof of part (i) of Theorem 0.1. By Remark 5.2, we may assume that X = t, in which case the assertion is nothing but [Ohk17,Theorem 4.19].…”

Section: Logarithmic Growth Filtrations For (ϕ ∇)-Modules Over R Bdmentioning

confidence: 99%

Section: Then Condition (I) Implies Condition (Ii) Moreover If K Is Perfect Then Condition (Ii) Implies Condition (I)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%