Fundamental Lemma 1 & 2

Object G = Object H
(Fundamental Lemma 2, FL2)

; G & H are objects in Grothendieck’s geometry.

Ngô Bảo Châu realised that the geometric objects needed for FL2 could be built out of the repertoire of mathematical physics, thus reversing Weil’s and Grothendieck’s original priorities: instead of using the results of counting about geometric objects to pin them down to motives by applying the equality in FL1 i.e.

Quantity G = Quantity H as not quantities themselves.