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Let be a smooth curve defined over the fraction field of a complete discrete valuation ring . We study a natural filtration of the special fiber of the Néron model of the Jacobian of by closed, unipotent subgroup schemes. We show that the jumps in this filtration only depend on the fiber type of the special fiber of the minimal regular model with strict normal crossings for over , and in particular are independent of the residue characteristic. Furthermore, we obtain information about...
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 embedded in its jacobian by an Albanese map; and (2) the...
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