We reinterpret a conjecture of Breuil on the locally analytic $mathrm{Ext}^1$ in a functorial way using $(varphi,Gamma)$-modules (possibly with $t$-torsion) over the Robba ring, making it more accurate. Then we prove several special or partial cases of this improved conjecture, notably for ${rm GL}_3(mathbb{Q}_p)$.
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