Kolyvagin's trace relations for Siegel sixfolds

In his earlier preprints the author offered a program of generalization of Kolyvagin's result of finiteness of SH to the case of some motives which are quotients of cohomology motives of Shimura and Drinfeld varieties. The present paper is devoted to the first step of this program—finding of an analog of Kolyvagin's trace relations. We find it for Siegel sixfolds and for the Hecke correspondences related to the matrices diag(1,1,1,p,p,p) and diag(p,1,1,p,p2,p2). This is the first non-trivial case for Shimura varieties. Some results for other types of Siegel varieties and Hecke correspondences are obtained.Ideas and methods of the present paper open a large new area of research: results given here constitute a tiny part of what can be done. Particularly, maybe it is possible to realize the program of generalization of Kolyvagin's result for the functional case (moduli varieties of Drinfeld modules and similar objects).