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 > On the local mod p representation attached to a modular form

## On the local mod p representation attached to a modular formAdd to your list(s) Download to your calendar using vCal - Kevin Buzzard (Imperial)
- Tuesday 22 January 2013, 16:15-17:15
- MR14.
If you have a question about this talk, please contact Teruyoshi Yoshida. There is a 2-dimensional p-adic Galois representation attached to any modular form which is an eigenform for the Hecke operators. One can reduce it mod p and get an even simpler object – a mod p Galois representation, which will have finite image. One would have thought that nowadays essentially everything was known about this representation, but actually there are still some dangling issues at p. For example – if I give you an explicit modular form (e.g. via its q-expansion), is the associated local mod p representation reducible or irreducible? This question is local, but still poorly understood. I will explain what little I know, most of which is joint work with Toby Gee. In what looks like a sledgehammer-cracking-a-nut approach, we invoke recent deep work of Breuil-Berger and others on the p-adic and mod p Langlands philosophy for GL(2) to get some concrete down-to-earth results. 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
- MR14
- Number Theory Seminar
- School of Physical Sciences
Note that ex-directory lists are not shown. |
## Other listsSir Edmund Hillary Memorial Lecture Electron Microscopy Group Conferences Mind-matter Unification Project (TCM Group, Cavendish Laboratory)## Other talksEdge-exchangeable graphs, sparsity, and power laws Unlocking the potential of synthetic biology to enhance human health Random walk models of networks: modeling and inferring complex dependence Bayesian Methods for Networks The Quest for Innovative Treatments in Psychiatry and Medicine: a personal perspective Nuclear fusion |