Annihilation of Selmer groups for monomial CM-extensions

作者：Nomura Jiro^*

来源：Journal of Number Theory, 2014, 144: 353-378.

DOI：10.1016/j.jnt.2014.05.008

• Abelian varieties
• Equivariant L-values
• Monomial groups

Let F/k be a finite Galois extension of number fields with Galois group G, and A an abelian variety over k. We fix an odd prime p. When G is isomorphic to the dihedral group of order 4p, assuming the Birch and Swinnerton-Dyer conjecture and some technical assumptions, we prove that the Pontryagin dual of the (classical) Selmer group Sel(p)(A(F))v is annihilated by some element in the center of the group ring Z(p)[G] which is constructed from equivariant h-values. More generally, we study the relation between the annihilation of Selmer groups for non-abelian extensions and that for abelian extensions.

• 出版日期2014-11