We present a generalization of the theory of local constant developed by B.Mazur and K. Rubin in order to cover the case of abelian varieties, withemphasis to abelian varieties with real multiplication. Let be an oddrational prime and let be an abelian -power extension. Assume that weare given a quadratic extension such that is a dihedral extensionand the abelian variety is defined over and polarizable. This theorycan be used to relate the rank of the -Selmer group of over to the rankof the -Selmer group of over .
Cite this article
Marco Adamo Seveso, The Arithmetic Theory of Local Constants for Abelian Varieties. Rend. Sem. Mat. Univ. Padova 127 (2012), pp. 17–39DOI 10.4171/RSMUP/127-2