March 31, 2024Open Access

The Rational Torsion Subgroup of J₀ (pʳ)

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Abstract

Let n=pʳ be a prime-power ideal of FqT with r 2. We study the rational torsion subgroup T (pʳ) of the Drinfeld modular Jacobian J₀ (pʳ). We prove that the prime-to-q (q-1) part of T (pʳ) is equal to that of the rational cuspidal divisor class group C (pʳ) of the Drinfeld modular curve X₀ (pʳ). As we completely computed the structure of C (pʳ), it also determines the structure of the prime-to-q (q-1) part of T (pʳ).

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Sheng-Yang Kevin Ho (Sun,) studied this question.

synapsesocial.com/papers/68e718f1b6db64358769250a https://doi.org/https://doi.org/10.48550/arxiv.2404.00738

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