Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9496527 | Journal of Number Theory | 2005 | 25 Pages |
Abstract
Let E be an elliptic curve over Q and â be an odd prime. Also, let K be a number field and assume that E has a semi-stable reduction at â. Under certain assumptions, we prove the vanishing of the Galois cohomology group H1(Gal(K(E[âi])/K),E[âi]) for all i⩾1. When K is an imaginary quadratic field with the usual Heegner assumption, this vanishing theorem enables us to extend a result of Kolyvagin, which finds a bound for the order of the â-primary part of Shafarevich-Tate groups of E over K. This bound is consistent with the prediction of Birch and Swinnerton-Dyer conjecture.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Byungchul Cha,