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Pré-Publication, Document De Travail Année : 2022

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

Résumé

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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Dates et versions

hal-02267548 , version 1 (19-08-2019)
hal-02267548 , version 2 (02-07-2021)
hal-02267548 , version 3 (09-01-2022)
hal-02267548 , version 4 (04-12-2022)
hal-02267548 , version 5 (11-10-2023)

Identifiants

  • HAL Id : hal-02267548 , version 3

Citer

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