1 results
Independence of
$\ell $-adic Galois representations over function fields
- Part of
-
- Journal:
- Compositio Mathematica / Volume 149 / Issue 7 / July 2013
- Published online by Cambridge University Press:
- 25 April 2013, pp. 1091-1107
- Print publication:
- July 2013
-
- Article
-
- You have access
- Export citation
-
Let
$K$ be a finitely generated extension of 
$\mathbb {Q}$. We consider the family of 
$\ell $-adic representations (
$\ell $ varies through the set of all prime numbers) of the absolute Galois group of 
$K$, attached to 
$\ell $-adic cohomology of a separated scheme of finite type over 
$K$. We prove that the fields cut out from the algebraic closure of 
$K$by the kernels of the representations of the family are linearly disjoint over a finite extension of K. This gives a positive answer to a question of Serre.
