The Weil pairing and the Hilbert symbol

  title={The Weil pairing and the Hilbert symbol},
  author={Everett W. Howe},
Let C be a geometrically irreducible curve over a field k, let k be an algebraic closure of k, and let m be any positive integer not divisible by the characteristic of k. The Jacobian variety J of C comes equipped with a principal p~ar ization A, which is in particular an isomorphism from J to its dual variety J . The polarization A gives us an isomorphism between the m-torsion J m of J and its Cartier dual, and this isomorphism turns the natural pairing Jm • Jm ~ l~m into the Weilpairing em:Jm… CONTINUE READING
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