University of Cambridge > Talks.cam > Number Theory Seminar > On the local mod p representation attached to a modular form

  Browse A-Z

Log in

University Account External (via Google)

🔐 Log In

Information on

Subscribing to talksdetails Finding a talkdetails Adding a talkdetails Disseminating talksdetails Help and Documentationdetails

ℹī¸ Information

On the local mod p representation attached to a modular form

Download to your calendar using vCal

  • UserKevin Buzzard (Imperial)
  • ClockTuesday 22 January 2013, 16:15-17:15
  • HouseMR14.

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:

Note that ex-directory lists are not shown.

Other lists

GR-04, English Faculty Building Type the title of a new list here Babraham Events

Other talks

Tea and Coffee Break Tea and Coffee Break Non-stationarity in structural dynamics, challenges and implications for modelling and structural health monitoring Title tbc Title TBC Afternoon Break
 

Š 2006-2025 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity