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Changed GSP to its Langlands dual
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Eins Null
Eins Null
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When are the $l$-local $p$-adic Galois representations of Siegel modular forms semistable? By this I mean $\rho_{f}: G_{\mathbb{Q}}\to \operatorname{GSp}_{2n}(\overline{\mathbb{Q}}_p)$$\rho_{f}: G_{\mathbb{Q}}\to \operatorname{GSpin}_{2n+1}(\overline{\mathbb{Q}}_p)$ restricted to the decomposition group at $l$. Is this controlled by the level? I am primarily interested in this when $l=p$ and $n=2$.

When are the $l$-local $p$-adic Galois representations of Siegel modular forms semistable? By this I mean $\rho_{f}: G_{\mathbb{Q}}\to \operatorname{GSp}_{2n}(\overline{\mathbb{Q}}_p)$ restricted to the decomposition group at $l$. Is this controlled by the level? I am primarily interested in this when $l=p$ and $n=2$.

When are the $l$-local $p$-adic Galois representations of Siegel modular forms semistable? By this I mean $\rho_{f}: G_{\mathbb{Q}}\to \operatorname{GSpin}_{2n+1}(\overline{\mathbb{Q}}_p)$ restricted to the decomposition group at $l$. Is this controlled by the level? I am primarily interested in this when $l=p$ and $n=2$.

Added nt.number-theory tag
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David Loeffler
David Loeffler
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When are the $l$-local $p$-adic Galois representations of Siegel modular forms semistable? By this I mean $\rho_{f}: G_{\mathbb{Q}}\to GSp_{2n}(\mathbb{Q}_p)$$\rho_{f}: G_{\mathbb{Q}}\to \operatorname{GSp}_{2n}(\overline{\mathbb{Q}}_p)$ restricted to the decomposition group at $l$. Is this controlled by the level? I am primarily interested in this when $l=p$ and $n=2$.

When are the $l$-local $p$-adic Galois representations of Siegel modular forms semistable? By this I mean $\rho_{f}: G_{\mathbb{Q}}\to GSp_{2n}(\mathbb{Q}_p)$ restricted to the decomposition group at $l$. Is this controlled by the level? I am primarily interested in this when $l=p$ and $n=2$.

When are the $l$-local $p$-adic Galois representations of Siegel modular forms semistable? By this I mean $\rho_{f}: G_{\mathbb{Q}}\to \operatorname{GSp}_{2n}(\overline{\mathbb{Q}}_p)$ restricted to the decomposition group at $l$. Is this controlled by the level? I am primarily interested in this when $l=p$ and $n=2$.

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Eins Null
Eins Null
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Semistability of local Siegel Galois rep:

When are the $l$-local $p$-adic Galois representations of Siegel modular forms semistable? By this I mean $\rho_{f}: G_{\mathbb{Q}}\to GSp_{2n}(\mathbb{Q}_p)$ restricted to the decomposition group at $l$. Is this controlled by the level? I am primarily interested in this when $l=p$ and $n=2$.