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M. Rapoport

Publications and source records attributed to M. Rapoport.

21 records · Page 2Linked to original sources
arXiv1997

Cycles on Siegel 3-folds and derivatives of Eisenstein series

We consider the Siegel modular variety of genus 2 and a p-integral model of it for a good prime p>2, which parametrizes principally polarized abelian varieties of dimension two with a level structure. We consider cycles on this model which are characterized by the existence of certain special endomorphisms, and their intersections. We characterize that part of the intersection which consists of isolated points in characteristic p only. Furthermore, we relate the (naive) intersection multiplicities of the cycles at isolated points to special values of derivatives of certain Eisenstein series on the metaplectic group in 8 variables.

alg-geom↗
arXiv1997

A geometric approach to the fundamental lemma for unitary groups

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.

alg-geom↗