Kolyvagin derivatives of modular points on elliptic curves
Lead Research Organisation:
University of Nottingham
Department Name: Sch of Mathematical Sciences
Abstract
"Using modular and integral representation theory and group cohomology, it is possible to generalise the derivative construction by Kolyvagin to non-abelian Galois groups. This can be applied to rational points on elliptic curves obtained from the modular parametrisation and it yields interesting cohomology classes that may bound Selmer groups for twists by different Artin representations than the ones generated by the points."
Organisations
People |
ORCID iD |
| Christian Wuthrich (Primary Supervisor) | |
| Richard Hatton (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N50970X/1 | 01/10/2016 | 30/09/2021 | |||
| 1800613 | Studentship | EP/N50970X/1 | 01/10/2016 | 30/09/2019 | Richard Hatton |
| Description | I have shown that for certain elliptic curves, there exists an element of prime power order in certain Selmer groups. |
| Exploitation Route | I would like to further expand on the result I have by relaxing the constraints I have on the elliptic curves with this property. This would require more research in the algebraic side of my work. |
| Sectors | Other |
| Description | 2nd Year Talk on the progress of my work |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Local |
| Primary Audience | Postgraduate students |
| Results and Impact | I gave an overview of my research on modular points on elliptic curves. The purpose was to let other people in department know my research, ensure that I had understood the work I had been completing and practising giving talks. |
| Year(s) Of Engagement Activity | 2018 |
| Description | Invited research talk as part of online lecture series |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Professional Practitioners |
| Results and Impact | I was invited by Dr Netan Dogra to give two talks, the first on the Birch and Swinnerton-Dyer Conjecture, and the second focussed on my research on modular points on elliptic curves. The aim was to introduce the subject to postgraduate students and share my findings with them. |
| Year(s) Of Engagement Activity | 2020 |
| URL | https://sites.google.com/site/netandogra/working-seminar |
| Description | Invited research talk at the Institute Camille-Jordan in Lyon |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | I was invited by Dr Xavier Francois Roblot to give a talk on my research on modular points on elliptic curves. The aim was to share my findings with other members of the mathematical community overseas. |
| Year(s) Of Engagement Activity | 2019 |
| Description | Invited research talk at the Junior Number Theory seminar at Kings College London |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Postgraduate students |
| Results and Impact | I was invited to give a talk on my research on modular points of elliptic curves. The aim was to share my findings with other members of the mathematical community and to increase my presentation portfolio. |
| Year(s) Of Engagement Activity | 2019 |
| Description | Young Researchers in Algebraic Number Theory Conference Talk |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | I gave an overview of my research on modular points on elliptic curves. The purpose was to let other people in the mathematical community know my research and to see if any other student's research area was linked to mine. |
| Year(s) Of Engagement Activity | 2018 |
| URL | http://y-rant.group.shef.ac.uk/ |