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Dear Vytas,

lemma 6.5 of my 2002 inventiones paper says that if $V$ is any de Rham representation all of whose HT weights are at least 1, then any extension of $Q_p$ by $V$ is itself de Rham. This holds for reps of $G_K$ where the residue field $k$ of $K$ can be any perfect field (not merely finite).

If $k$ is finite, then this was well-known before and follows from the results of Bloch and Kato (which I think you should quote). See proposition 1.28 of Nekovar's "On $p$-adic height pairings" where this is stated explicitly and proved using BK's comuptationscomputations.

EDIT: see also the "Proposition" on page 196 of Perrin-Riou's "Représentations $p$-adiques ordinaires". It predates Nekovar's paper, and although the result is less strong, it's enough for what you need.

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Dear Vytas,

lemma 6.5 of my 2002 inventiones paper says that if $V$ is any de Rham representation all of whose HT weights are at least 1, then any extension of $Q_p$ by $V$ is itself de Rham. This holds for reps of $G_K$ where the residue field $k$ of $K$ can be any perfect field (not merely finite).

If $k$ is finite, then this was well-known before and follows from the results of Bloch and Kato (which I think you should quote). See proposition 1.28 of Nekovar's "On $p$-adic height pairings" where this is stated explicitly and proved using BK's comuptations.

EDIT: see also the "Proposition" on page 196 of Perrin-Riou's "Représentations $p$-adiques ordinaires". It predates Nekovar's paper, and although the result is less strong, it's enough for what you need.

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Dear Vytas,

lemma 6.5 of my 2002 inventiones paper says that if $V$ is any de Rham representation all of whose HT weights are at least 1, then any extension of $Q_p$ by $V$ is itself de Rham. This holds for reps of $G_K$ where the residue field $k$ of $K$ can be any perfect field (not merely finite).

If $k$ is finite, then this was well-known before and follows from the results of Bloch and Kato (which I think you should quote). See proposition 1.28 of Nekovar's "On $p$-adic height pairings" where this is stated explicitly and proved using BK's comuptations.