### Galois theory and torsion points on curves

Matthew H. Baker, Kenneth A. Ribet (2003)

Journal de théorie des nombres de Bordeaux

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In this paper, we survey some Galois-theoretic techniques for studying torsion points on curves. In particular, we give new proofs of some results of A. Tamagawa and the present authors for studying torsion points on curves with “ordinary good” or “ordinary semistable” reduction at a given prime. We also give new proofs of : (1) the Manin-Mumford conjecture : there are only finitely many torsion points lying on a curve of genus at least $2$ embedded in its jacobian by an Albanese map;...