Filtrations de type Hasse-Arf et monodromie p-adique

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One proves the Crew-Tsuzuki \"p-adic local monodromy conjecture\" (for local fields of characteristic p>0).

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Relative p-adic Hodge theory, II: Imperfect period rings (2016, background): “• Berger’s original proof in [12] of Fontaine’s conjecture that de Rham representations are potentially semistable involves a reduction to a monodromy theorem for p-adic differential equations over the Robba ring (see [4, 69, 90]).”
Slope filtrations (2008, methodology): “[4] Let us assume moreover that for any n,”
A p-adic local monodromy theorem (2001, methodology): “Note that Theorem 1.1 itself has been established independently by Andr´e [ A2 ] and by Mebkhout [M].”
An introduction to the theory of p-adic representations (2002, result): “The above theorem is proved independently in Andr´e’s [ 2 ], Mebkhout’s [64] and Kedlaya’s [59].”
Semistable reduction for overconvergent $F$-isocrystals I: Unipotence and logarithmic extensions (2004, background): “The p-adic local monodromy theorem of André [And02], Mebkhout [Meb02], and the present author [Ked04a] implies a strong statement in the direction of Conjecture 7.1.2.”
Slope filtrations revisited (2005, methodology): “We note, for now in passing, that Crew’s conjecture has also been proved by André [1] and by Mebkhout [28], using the Christol-Mebkhout index theory for p-adic differential equations; for more on the relative merits of these proofs, see Remark 7.”