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Explicit Computation of a Galois Representation Attached to an Eigenform Over $${\text {SL}}_3$$ SL 3 from the $${{\text {H}}}_{\acute{\mathrm{e}}\mathrm{t}}^2$$ H e ´ t 2 of a Surface
Foundations of Computational Mathematics ( IF 2.5 ) Pub Date : 2022-01-11 , DOI: 10.1007/s10208-021-09505-z
Nicolas Mascot 1
Affiliation  

We describe a method to compute mod \(\ell \) Galois representations contained in the \({{\text {H}}}_{\acute{\mathrm{e}}\mathrm{t}}^2\) of surfaces. We apply this method to the case of a representation with values in \({\text {GL}}_3(\mathbb {F}_9)\) attached to an eigenform over a congruence subgroup of \({\text {SL}}_3\). We obtain, in particular, a polynomial with Galois group isomorphic to the simple group \({\text {PSU}}_3(\mathbb {F}_9)\) and ramified at 2 and 3 only.



中文翻译:

从 $${{\text {H}}}_{\acute{\m​​athrm{e}}\ mathrm{t}}^2$$ 表面的 H e ´ t 2

我们描述了一种计算包含在\({{\text {H}}}_{\acute{\m​​athrm{e}}\mathrm{t}}^2\) 中的mod  \(\ell \)伽罗瓦表示的方法 的表面。我们将此方法应用于将 \({\text {GL}}_3(\mathbb {F}_9)\) 中的值附加到 \({\text {SL} }_3\)。特别地,我们获得了一个多项式,其伽罗瓦群同构于简单群 \({\text {PSU}}_3(\mathbb {F}_9)\)并且仅在 2 和 3 处分枝。

更新日期:2022-01-12
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