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- W4300594292 abstract "We study the rational torsion subgroup of the modular Jacobian <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>N</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> </mml:math> for N a square-free integer. We give a proof of a result of Ohta on a generalization of Ogg’s conjecture: For a prime number <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:mrow> <mml:mi>p</mml:mi> <mml:mi mathvariant=normal>∤</mml:mi> <mml:mn>6</mml:mn> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> , the p -primary part of the rational torsion subgroup equals that of the cuspidal subgroup. Whereas previous proofs of this result used explicit computations of the cardinalities of these groups, we instead use their structure as modules for the Hecke algebra." @default.
- W4300594292 created "2022-10-03" @default.
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- W4300594292 date "2022-10-03" @default.
- W4300594292 modified "2023-09-29" @default.
- W4300594292 title "Another look at rational torsion of modular Jacobians" @default.
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- W4300594292 doi "https://doi.org/10.1073/pnas.2210032119" @default.
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