p -adic Differential Equations: The p -adic local monodromy theorem: proof

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Classification of two-dimensional split trianguline representations of p-adic fields (2008, methodology): “Proof. Because Im(f) is finite torsion free Be ⊗Qp E-module, it is free by the remark after Lemma 2.4 [ Ke04 ].”
Semistable reduction for overconvergent F-isocrystals, IV: local semistable reduction at nonmonomial valuations (2006, methodology): “1]; note that this depends on the generalized slope filtration theorem of [13], not just on the original form of the theorem of [11].”
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]).”
Relative P-adic Hodge Theory: Foundations (2013, background): “) In [67], one starts with the Robba ring of germs of analytic functions on open annuli of outer radius 1 over a p-adic field, and then passes to a certain “algebraic closure” thereof.”
Construction de (φ,Γ)-modules: représentations p-adiques et B-paires (2008, unknown): “5 de [Kedlaya 2004] montre que l’on peut écrire M = M ·M† avec M ∈GLd(B+rig,K ) et M † ∈ GLd(BK ).”