COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Number Theory Seminar > Completely faithful Selmer groups over GL(2)-extensions

## Completely faithful Selmer groups over GL(2)-extensionsAdd to your list(s) Download to your calendar using vCal - Gergely Zábrádi (Eötvös Loránd University)
- Tuesday 18 February 2014, 16:15-17:15
- MR13.
If you have a question about this talk, please contact James Newton. Let E and A be two elliptic curves, both defined over Q, and p>3 be a good ordinary prime for E. Assume that A has no complex multiplication so that the Galois group G of the extension F_\infty/Q=Q(A[p^{\infty}])/Q is an open subgroup of GL_2(Z_p). The aim of the talk is to investigate the dual Selmer group of E over F_\infty. Under certain technical hypotheses we prove that its characteristic element satisfies a functional equation. Assume further that there exists a prime q (different from p) such that (i) A has potentially multiplicative reduction at q and (ii) all the p-power division points of E are defined over the completion of F_\infty at a prime above q. As a consequence we show that the dual Selmer X(E/F_\infty) cannot be annihilated by any element in the centre of \Lambda(G). In particular, if in addition the \Lambda(H)-rank of X(E/F_\infty) equals 1 then X(E/F_\infty) is completely faithful. Unfortunately, this latter condition is never satisfied if E=A, but we do have examples of completely faithful Selmer groups when E is different from A. This is joint work in progress with T. Backhausz. This talk is part of the Number Theory Seminar series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- Hanchen DaDaDash
- Interested Talks
- MR13
- Number Theory Seminar
- School of Physical Sciences
- bld31
Note that ex-directory lists are not shown. |
## Other listsHomerton Seminars King's Review Salons The Sackler Lectures## Other talksNew approaches to old problems: controlling pathogenic protozoan parasites of poultry Autumn Cactus & Succulent Show What is the History of the Book? Visual Analytics for High-Dimensional Data Exploration and Engineering Design Respiratory Problems Climate Change: Engaging Youth |