School of Mathematics Seminars and Lectures
Galois representations with open image
by Prof. Ralph Greenberg (University of Washington, USA)
Tuesday, July 10, 2012
from
to
(Asia/Kolkata)
at Colaba Campus ( AG-77 )
at Colaba Campus ( AG-77 )
Description |
Suppose that p is a prime and that n \ge 1. Let G_{\bf Q} = Gal(\overline{\bf Q}/{\bf Q}) be the absolute Galois group of {\bf Q}. Let {\bf Z}_p denote the ring of p-adic integers. Our purpose in this talk is to describe a way of constructing continuous representations \rho: G_{\bf Q} ~\longrightarrow ~ GL_n({\bf Z}_p) whose image is open. This means that the image of $\rho$ has finite index in GL_n({\bf Z}_p). We can do this for many pairs $(n,p)$. One typical result is the following: Proposition: Suppose that p is a regular prime and that p \ge 4\big[ \frac{n}{2} \big] + 1. Then there exists a continuous representation \rho as above with open image. |