Abstract
We give Hrushovski’s proof of the (extended) Manin-Mumford conjecture over number fields. Recall that the Manin-Mumford conjecture states that if X is a nonsingular projective curve of genus > 1 over an algebraically closed field of characteristic 0, and A is the Jacobian variety of X then X ∩ Tor (A) is finite (where Tor (A) denotes the group of torsion points of A). This is of course a special case of the Mordell-Lang conjecture. Raynaud [8] proved that if A is an abelian variety (in characteristic 0) and X is a subvariety of A then X ∩ Tor(A) is a finite union of cosets (proving in particular Manin-Mumford). Hindry [3] proved the same thing, but with A an arbitrary commutative algebraic group.
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© 1997 Springer Science+Business Media Dordrecht
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Pillay, A. (1997). ACFA and the Manin-Mumford Conjecture. In: Hart, B.T., Lachlan, A.H., Valeriote, M.A. (eds) Algebraic Model Theory. NATO ASI Series, vol 496. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8923-9_9
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DOI: https://doi.org/10.1007/978-94-015-8923-9_9
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