# Reduction to Lie algebra version of fundamental lemma?

Ngo famously proved the Langlands-Shelstad fundamental lemma for Lie algebras using the geometry of the Hitchin fibration.

For the purposes of the trace formula, one actually needs the fundamental lemma for the group. In his ICM notes, Ngo states that Waldspurger shows how to reduce the group statement to the Lie algebra statement, but the reference is not clear (to me at least).

My question is

Where is this reduction discussed? A precise reference would be great.

In lieu of the reference, I would also gladly accept a sketch of the reduction:

How does this reduction work?

• Both transferring between all t.n. elements in the Lie algebra and all t.u. elements in the group, and transferring between equi-characteristic and mixed-characteristic fields, require that $p$ be very large (the bound in the latter case being totally ineffective). Is that just the state of things now, that this reduction is only available for very large $p$, or are there ways around it? – LSpice Sep 30 '19 at 1:24
You can find it in Waldspurger's paper titled Le lemme fondamental implique le transfert.