ACFA and the Manin-Mumford Conjecture

  • Anand Pillay
Part of the NATO ASI Series book series (ASIC, volume 496)

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.

Keywords

Irreducible Component Abelian Variety Number Field Finite Union Residue Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Anand Pillay
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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