The Shafarevich-Tate conjecture for pencils of elliptic curves onK3 surfaces
✍ Scribed by M. Artin; H. P. F. Swinnerton-Dyer
- Publisher
- Springer-Verlag
- Year
- 1973
- Tongue
- English
- Weight
- 784 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0020-9910
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Let E be an elliptic curve over ] be an irreducible polynomial of odd degree, and let K =F ( √ d). Assume (p) remains prime in K. We prove the analogue of the formula of Gross for the special value L(E⊗ F K, 1). As a consequence, we obtain a formula for the order of the Tate-Shafarevich group I(E/K
We compute the ,-Selmer group for a family of elliptic curves, where , is an isogeny of degree 5, then find a practical formula for the Cassels Tate pairing on the ,-Selmer groups and use it to show that a particular family of elliptic curves have non-trivial 5-torsion in their Shafarevich Tate grou