The Weil pairing and the Hilbert symbol

@inproceedings{Howe2005TheWP,
  title={The Weil pairing and the Hilbert symbol},
  author={Everett W. Howe},
  year={2005}
}
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
9 Citations
6 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-6 of 6 references

Elliptic curves (Grad

  • D. Husem611er
  • Texts Math.,
  • 1987
Highly Influential
7 Excerpts

Algebraic groups and class fields (Grad

  • Serre, J.-P
  • Texts Math.,
  • 1988

1-I. (eds.): Arithmetic geometry (pp

  • Milne, J. Silverman
  • 1986
2 Excerpts

The arithmetic of elliptic curves (Grad

  • J. H. Silvemmn
  • Texts Math., vol. 106) Berlin Heidelberg New York…
  • 1986

Abelian varieties

  • S. Lang
  • New York: Interscience
  • 1959
3 Excerpts

Ober das Reziprozita'tsgesatz in relativ-zyklischen algebraischen Funktionk/Srpem mit endlichem Konstantenk6rper

  • Sehmidt, L H.
  • Math. Z. 40, 94-109
  • 1936
1 Excerpt

Similar Papers

Loading similar papers…