The Manin–Mumford conjecture for Drinfeld modules
The Manin–Mumford conjecture for Drinfeld modules
Let be a function field of transcendence degree over , and let be a Drinfeld module. Let and let be an irreducible -subvariety of . The torsion points for are points of whose coordinates are torsion points for the diagonal action. Manin–Mumford conjecture for Drinfeld modules. If the set of torsion points for is dense in , then there exist a torsion point and a -subvariety , invariant under a nonzero endomorphism of , such that
This is presented as a weak form of the Bogomolov conjecture. The examples in the supplied context indicate that, in finite characteristic, invariance under an endomorphism is the sharp conclusion, while the source suggests a stronger formulation may hold in generic characteristic; no resolution of this stated conjecture is supplied.
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Sources & referencesView supporting material
Primary source
Dragos Ghioca, “Points of small height on varieties defined over a function field”, arXiv:math/0505001 (2005).
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