A geometric approach to the fundamental lemma for unitary groups
| dc.creator | Laumon, G. | |
| dc.creator | Rapoport, M. | |
| dc.date | 1997-11-19 | |
| dc.date.accessioned | 2026-07-07T01:51:18Z | |
| dc.date.available | 2026-07-07T01:51:18Z | |
| dc.description | 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. | |
| dc.description | 44 pages, Plain TeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9711021 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9711021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/265 | |
| dc.subject | Algebraic Geometry | |
| dc.title | A geometric approach to the fundamental lemma for unitary groups | |
| dc.type | text |