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Relations between Jacobians of modular curves of level \(p^2\). (English) Zbl 1156.11323
Summary: We derive a relation between induced representations on the group \(\text{GL}_2(\mathbb Z/p^2\mathbb Z)\) which implies a relation between the Jacobians of certain modular curves of level \(p^2\). The motivation for the construction of this relation is the determination of the applicability of Mazur’s method to the modular curve associated to the normalizer of a non-split Cartan subgroup of \(\text{GL}_2(\mathbb Z/p^2\mathbb Z)\).
MSC:
11G18 Arithmetic aspects of modular and Shimura varieties
14G35 Modular and Shimura varieties
14H40 Jacobians, Prym varieties
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References:
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