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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > A uniform open image theorem for $ll$-adic representations (joint work with Akio Tamagawa - R.I.M.S.)

## A uniform open image theorem for $ll$-adic representations (joint work with Akio Tamagawa - R.I.M.S.)Add to your list(s) Download to your calendar using vCal - Cadoret, A (Bordeaux 1)
- Friday 28 August 2009, 14:00-15:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Non-Abelian Fundamental Groups in Arithmetic Geometry In this talk, we extend some of the results presented in Tamagawa’s talk to more general $ll$-adic representations.\
indent Let $k$ be a finitely generated field of characteristic $0$, $X$ a smooth, separated, geometrically connected curve over $k$ with generic point $ta$. A $ll$-adic representation $
ho:pi_{1}(X)
ightarrow hbox{
m GL} ightarrowpi_{1}(X_{kappa(x)})$
of the canonical restriction epimorphism $pi_{1}(X_{kappa(x)})
ightarrow Gamma_{kappa(x)}$
(here, $kappa(x)$ denotes the field of definition of $x$) so one can define the closed subgroup
$G_{x}:=
ho rc x(Gamma_{kappa(x)}) ubset G$ (up to inner automorphisms).\ indent The main result I am going to discuss is the following
uniform open image theorem. extit{Under the above assumptions, for any
representation $
ho:pi_{1}(X)
ightarrow hbox{
m GL} This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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