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$\overline{\mathbb F}_l$-Galois semi-simplicity and level raising

Abstract : For a maximal ideal $\mathfrak m$ of some anemic Hecke algebra $\mathbb{T}^S$, associated to an irreducible Galois $\overline{\mathbb F}_l$-representation of dimension $d$, on can also define a Galois $\mathbb{F}_{\mathfrak m}^S$-representation $\rho_{\mathfrak m}$. The length of $\rho_{\mathfrak m} \otimes_{\overline{\mathbb Z}_l} \overline{\mathbb F}_l$ is equal to the number of prime ideals $\widetilde{\mathfrak m} \subset \mathfrak m$ and we try to translate some of the properties of $\bigl \{ \widetilde{\mathfrak m} \subset \mathfrak m \bigr \}$ into those of $\rho_{\mathfrak m} \otimes_{\overline{\mathbb Z}_l} \overline{\math bb F}_l$. For example the level raising (or lowering) property is encoded by the non semi-simplicity of $\rho_{\mathfrak m} \otimes_{\overline{\mathbb Z}_l} \overline{\mathbb F}_l$.
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https://hal.archives-ouvertes.fr/hal-02267548
Contributor : Pascal Boyer Connect in order to contact the contributor
Submitted on : Sunday, January 9, 2022 - 4:00:30 PM
Last modification on : Thursday, January 13, 2022 - 12:00:30 PM

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  • HAL Id : hal-02267548, version 3

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Pascal Boyer. $\overline{\mathbb F}_l$-Galois semi-simplicity and level raising. 2022. ⟨hal-02267548v3⟩

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