  We consider from a geometric point of view the conjectural fundamental lemma
of Langlands and Shelstad for unitary groups over a local field of positive
characteristic. We introduce projective algebraic varieties over the finite
residue field $k$ and interpret the conjecture in this case as a remarkable
identity between the number of $k$-rational points of them. We prove the
corresponding identity for the numbers of $k_f$-rational points, for any
extension of even degree $f$ of $k$. The proof uses the local intersection
theory on a regular surface and Deligne's theory of intersection multiplicities
with weights. We also discuss a possible descent argument that uses $\ell$-adic
cohomology to treat extensions of odd degree as well.
