Kolyvagin's trace relations for Siegel sixfolds

In his earlier paper 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 varieties. The present paper is devoted to the first step of this program – finding of an analog of Kolyvagin’s trace relations for Siegel sixfolds and for the Hecke correspondence related to the matrix diag $(p,1,1,p,p^2,p^2)$. This is the first non-trivial case where we can expect that this program can be realised. 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.