Vanishing of some Galois cohomology groups for elliptic curves

Lawson, Tyler; Wuthrich, Christian

Abstract

Let E/Q be an elliptic curve and p be a prime number, and let G be the Galois group of the extension of Q obtained by adjoining the coordinates of the p-torsion points on E. We determine all cases when the Galois cohomology group H1(G;E[p] does not vanish, and investigate the analogous question for E[pi] when i > 1. We include an application to the verification of certain cases of the Birch and Swinnerton-Dyer conjecture, and another application to the Grunwald-Wang problem for elliptic curves.

Citation

Lawson, T., & Wuthrich, C. (2016). Vanishing of some Galois cohomology groups for elliptic curves. In D. Loeffler, & S. L. Zerbes (Eds.), Elliptic curves, modular forms and Iwasawa theory: in honour of John H. Coates' 70th birthday, Cambridge, UK, March 2015. Springer

• Acceptance Date: Jan 1, 2017
• Publication Date: Jan 1, 2016
• Deposit Date: Feb 21, 2017
• Peer Reviewed: Peer Reviewed
• Issue: 188
• Series Title: Springer proceedings in mathematics & statistics
• Book Title: Elliptic curves, modular forms and Iwasawa theory: in honour of John H. Coates' 70th birthday, Cambridge, UK, March 2015
• ISBN: 978-3-319-45032-2
• Public URL: https://nottingham-repository.worktribe.com/output/980152
• Related Public URLs: http://www.springer.com/gb/book/9783319450315
• Additional Information: DOI of book: 10.1007/978-3-319-45032-2
• Contract Date: Feb 21, 2017