Finding Large Selmer Rank via an Arithmetic Theory of Local Constants

  title={Finding Large Selmer Rank via an Arithmetic Theory of Local Constants},
  author={Barry Mazur and Karl Rubin},
We obtain lower bounds for Selmer ranks of elliptic curves over dihedral extensions of number fields. Suppose K/k is a quadratic extension of number fields, E is an elliptic curve defined over k, and p is an odd prime. Let K− denote the maximal abelian p-extension of K that is unramified at all primes where E has bad reduction and that is Galois over k with dihedral Galois group (i.e., the generator c of Gal(K/k) acts on Gal(K−/K) by inversion). We prove (under mild hypotheses on p) that if the… CONTINUE READING
Highly Cited
This paper has 26 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.
19 Citations
18 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 18 references

The Heegner point Kolyvagin system

  • B. Howard
  • Compositio Math
  • 2004

A generalisation of the Cassels-Tate pairing

  • M. Flach
  • J. Reine Angew. Math
  • 1990

Adeles and algebraic groups

  • A. Weil
  • Progress in Math. 23,
  • 1982

Similar Papers

Loading similar papers…