Galois Theory and Torsion Points on Curves

  title={Galois Theory and Torsion Points on Curves},
  author={Matthew H. Baker and Kenneth Alan Ribet},
We begin with a brief history of the problem of determining the set of points of a curve that map to torsion points of the curve’s Jacobian. Let K be a number field, and suppose that X/K is an algebraic curve of genus g ≥ 2. Assume, furthermore, that X is embedded in its Jacobian variety J via a K-rational Albanese map i; thus there is a K-rational divisor D of degree one on X such that i = iD : X ↪→ J is defined on K-valued points by the rule i(P ) = [(P )−D], where [ · ] denotes the linear… CONTINUE READING