In Grothendieck's *Esquisse* he claims that the action of
$$\text{Gal}(\mathbb Q)\to\text{Out}(\pi_1(M_{1,1})=\text{Out}(\widehat{SL(2,Z)})$$
obtained from the homotopy exact sequence of the étale fundamental group contains, after abelianization, all abelian $\ell$-adic representations defined by Jacobians and generalised Jacobians of algebraic curves defined over number fields. My questions (which might be hopelessly broad and misguided) are the following:

- How can one show this?
- Has any work been done extending this idea? A list of references is most welcome.

The original text is the following paragraph:

...from the point of view of Galois-Teichmuller theory, $SL(2,Z)$ can be considered as the fundamental “building block” of the "Teichmuller tower". The element of the structure of $SL(2,Z)$ which fascinates me above all is of course the outer action of Gal$(\mathbb Q)$ on its profinite compactification. By Bielyi’s theorem, taking the profinite compactifications of subgroups of finite index of $SL(2,Z)$, and the induced outer action (up to also passing to an open subgroup of Gal$(\mathbb Q)$),

we essentially find the fundamental groups of all algebraic curves(not necessarily compact)defined over number fields$K$, and the outer action of Gal$(K)$ on them – at least it is true that every such fundamental group appears as a quotient of one of the first groups (*). Taking the “anabelian yoga” (which remains conjectural) into account, which says that an anabelian algebraic curve over a number field $K$ (finite extension of $\mathbb Q$) is known up to isomorphism when we know its mixed fundamental group (or what comes to the same thing, the outer action of Gal($K$) on its profinite geometric fundamental group), we can thus say thatall algebraic curves defined over number fields are “contained” in the profinite compactification $\widehat{SL(2, Z)}$, and in the knowledge of a certain subgroup Gal$(\mathbb Q)$ of its group of outer automorphisms! Passing to the abelianisations of the preceding fundamental groups, we see in particular that all the abelian $\ell$-adic representations dear to Tate and his circle, defined by Jacobians and generalised Jacobians of algebraic curves defined over number fields, are contained in this single action of Gal$(\mathbb Q)$ on the anabelian profinite group $\widehat{SL(2, Z)}$!