Cuspidal divisor group conjecture for Drinfeld modular Jacobians
Cuspidal divisor group conjecture for Drinfeld modular Jacobians
Let be the ring of functions regular away from a fixed place at infinity, and let be a non-zero square-free ideal. Let be the smooth projective Drinfeld modular curve, let be its Jacobian, let be the subgroup generated by classes of divisors for cusps of , and let , where is the function field of . For square-free , the cusps are -rational, so . Drinfeld modular cuspidal torsion conjecture. For every square-free ideal , the two groups are equal:
This is proposed as the Drinfeld-modular analogue of the generalized Ogg conjecture. The source gives no resolution status for the assertion.
Sources & referencesView supporting material
Primary source
Mihran Papikian and Fu-Tsun Wei, “The rational torsion subgroups of Drinfeld modular Jacobians and Eisenstein pseudo-harmonic cochains”, arXiv:1512.00586 (2015).
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