Let $K$ be a finite extension of $\mathbb{Q}_p$ and $L$ be a finite Galois extension of $K$. Let $V$ be a $p$-adic representation of $G_L$ Let $D$ be the $(\varphi, \Gamma)$-module associated to $V$ by Fontaine's functor. Is there an easy way to describe the $(\varphi, \Gamma)$-module associated to $Ind_{G_L}^{G_K}$ Ind_{G_L}^{G_K} V$ in terms of $D$ ?
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Induced representations and $(\varphi, \Gamma)-modulesLet $K$ be a finite extension of $\mathbb{Q}_p$ and $L$ be a finite Galois extension of $K$. Let $V$ be a $p$-adic representation of $G_L$ Let $D$ be the $(\varphi, \Gamma)$-module associated to $V$ by Fontaine's functor. Is there an easy way to describe the $(\varphi, \Gamma)$-module associated to $Ind_{G_L}^{G_K}$ in terms of $D$ ?
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