A geometric approach to the fundamental lemma for unitary groups
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 November 1997
 DOI:
 10.48550/arXiv.alggeom/9711021
 arXiv:
 arXiv:alggeom/9711021
 Bibcode:
 1997alg.geom.11021L
 Keywords:

 Algebraic Geometry
 EPrint:
 44 pages, Plain TeX