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On the Q-rational cuspidal subgroup and the component group ofJ 0(p r)

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Abstract

Forp≥3 a prime, we compute theQ-rational cuspidal subgroupC(p r) of the JacobianJ 0(p r) of the modular curveX 0(p r). This result is then applied to determine the component group Φ p r of the Néron model ofJ 0(p r) overZ p . This extends results of Lorenzini [7]. We also study the action of the Atkin-Lehner involution on thep-primary part ofC(p r), as well as the effect of degeneracy maps on the component groups.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 119260, Singapore

    San Ling

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  1. San Ling
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Correspondence to San Ling.

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Ling, S. On the Q-rational cuspidal subgroup and the component group ofJ 0(p r). Isr. J. Math. 99, 29–54 (1997). https://doi.org/10.1007/BF02760675

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  • DOI: https://doi.org/10.1007/BF02760675

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