All Questions

Let $K_S$ denote the maximal extension of $\mathbb{Q}$, unramified outside a finite set of primes $S$, and let $G_S$ denote the Galois group of $K_S/\mathbb{Q}$. It is known that for any finitely ...

Assume that semi-simplicity of the Galois action on $\ell$-adic cohomology of all smooth projective varieties over finite fields, were known. Can one deduce that the Galois action on $\ell$-adic ...