The Drinfeld analogue of Ogg's Shimura-subgroup conjecture

Let p\mathfrak{p} be a prime of AA, let J0(p)J_0(\mathfrak{p}) be the Jacobian of the Drinfeld modular curve X0(p)X_0(\mathfrak{p}), let S(p)\mathcal{S}(\mathfrak{p}) be the Shimura subgroup, and let M(p)\mathcal{M}(\mathfrak{p}) be the maximal μ\mu-type subgroup of J0(p)J_0(\mathfrak{p}). Drinfeld Shimura-subgroup conjecture.

M(p)=S(p).\mathcal{M}(\mathfrak{p})=\mathcal{S}(\mathfrak{p}).

This is the Drinfeld analogue of Ogg's conjecture for the Shimura subgroup. The supplied text says that this prime-level conjecture was proved by Ambrus Pál.

Sources & referencesView supporting material

Primary source

Cécile Armana, Sheng-Yang Kevin Ho and Mihran Papikian, “Ogg's conjectures over function fields”, arXiv:2410.05502 (2024).

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