On the torsion of Jacobians of principal modular curves of level 3n |
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Authors: | Matthew Papanikolas Christopher Rasmussen |
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Affiliation: | (1) Department of Mathematics, Texas A&M University, College Station, TX 77843, USA;(2) Department of Mathematics, Rice University, Houston, TX 77005, USA |
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Abstract: | We demonstrate that the 3-power torsion points of the Jacobians of the principal modular curves X(3n) are fixed by the kernel of the canonical outer Galois representation of the pro-3 fundamental group of the projective line minus three points. The proof proceeds by demonstrating the curves in question satisfy a two-part criterion given by Anderson and Ihara. Two proofs of the second part of the criterion are provided; the first relies on a theorem of Shimura, while the second uses the moduli interpretation. Received: 30 September 2005 |
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Keywords: | 11G18 11G30 14H30 |
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