Let n be a square-free ideal of Fq[ T]. We study the rational torsion subgroup of the Jacobian variety J0(n) of the Drinfeld modular curve X0(n). We prove that for any prime number ℓ not dividing q(q- 1) , the ℓ-primary part of this group coincides with that of the cuspidal divisor class group. We further determine the structure of the ℓ-primary part of the cuspidal divisor class group for any prime ℓ not dividing q- 1.
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