Cycles on Siegel threefolds 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 abelia n varieties of dimension two with a level structure. We consider algebraic cycles on this model which are characterized by the existence of certain sp ecial endomorphisms, and their intersections. We characterize that part of the intersection which consists of isolated points in characteristic ii onl y. Furthermore, we relate the (naive) intersection multiplicities of the cy cles at isolated points to special values of derivatives of certain Eisenst ein series on the metaplectic group in 8 variables. (C) 2000 Editions scien tifiques et medicales Elsevier SAS.