by
Prof.Ralph Greenberg(University of Washington, USA)
→
Asia/Kolkata
AG-77 (Colaba Campus)
AG-77
Colaba Campus
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.
