Poonen's uniform boundedness conjecture for torsion of Drinfeld modules
Poonen's uniform boundedness conjecture for torsion of Drinfeld modules
Fix , , and . Let range over extensions of of degree at most , and let range over rank- Drinfeld -modules over . Poonen's Drinfeld-module uniform boundedness conjecture. The cardinalities are uniformly bounded. For rank , equivalently, there is a constant such that whenever and , the curve has no -rational points. This is the Drinfeld-module analogue of uniform boundedness for torsion of elliptic curves and abelian varieties. The supplied text gives no resolution.
Sources & referencesView supporting material
Primary source
Cécile Armana, Sheng-Yang Kevin Ho and Mihran Papikian, “Ogg's conjectures over function fields”, arXiv:2410.05502 (2024).
Additional references
3 papers in this index state this conjecture (1995–2024). The statement above is taken from the most recent of them; the others are arXiv:1210.3059, arXiv:math/9507217.
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