I don't know of a reference that discusses this particular example. For generalities, Wikipedia has a pretty good article on formal group laws (first hit on Google), together with some references.

Sorry, I thought perhaps there was an update to the discussion somewhere else, and he had mistakenly linked to the older post.

When you say, "quite recently," do you mean August 2007?

How do you make a natural transformation between a covariant and a contravariant functor?

I recommend replacing "local systems" with "G-local systems".

A loop in this setting is a map from a scheme with a "cyclic" fundamental group. Finite fields have this property, so their spectra can be viewed as circles. For Spec Z, the only interesting loops we see are the canonical maps from spectra of finite fields. One has an analogy between integration of differentials and parallel transport along connections, so we are determining how a vector bundle (our l-adic sheaf) is transformed as we follow flat sections around a "circle".

@KMB: Let f be the identity on the cuspidal cubic X=Y=Spec k[x,y]/(y^2-x^3), and let g be the normalization from A^1. Then there is no factorization, since k[x] doesn't map to k[x^2,x^3] in a way that commutes with the reverse inclusion.

Regarding the simple bivectors question, see the last paragraph of David Speyer's answer. One can take linear combinations of bivectors, but this does not preserve simplicity.

I was looking at free parameters in the full Weierstrass cubic form, but you're right that it is a poor choice. I will try to change it appropriately.

There is some discussion in the comments of that blog post about the formal version of this question. Kenny's comment (near the beginning) is especially illuminating, concerning technical difficulties.

The notion of Lie group requires the use of manifolds, so your constraint does not seem to make sense. In the absence of a clarifying edit, I'd suggest that this question be closed.

The revised version of that sentence is much clearer, thanks. Unfortunately, I still get a headache whenever the word "descent" is used.