Kolyvagin’s trace relations for Siegel sixfolds. (English) Zbl 1218.14029
This paper is concerned with a generalization of Kolyvagin’s result on the finiteness of the Tate-Shafarevich group and of the group of rational points of modular elliptic curves over \(\mathbb Q\) of analytic rank 0 to the case of some submotives of higher dimensional Shimura varieties or Drinfeld modular varieties. The author obtains an analog of Kolyvagin’s trace relations for Siegel sixfolds and for Hecke correspondences related to the matrices \(\text{diag} (1,1,1,p,p,p)\) and \(\text{diag} (p,1,1,p,p^2,p^3)\). He suggests that the methods adopted in this paper can be used for more general cases, including the functional case.
Reviewer: Min Ho Lee (Cedar Falls)
References:
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