The Arithmetic Theory of Local Constants for Abelian Varieties

  • Marco Adamo Seveso

    Università degli Studi di Milano, Italy

Abstract

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, with emphasis to abelian varieties with real multiplication. Let be an odd rational prime and let be an abelian -power extension. Assume that we are given a quadratic extension such that is a dihedral extension and the abelian variety is defined over and polarizable. This theory can be used to relate the rank of the -Selmer group of over to the rank of 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. 17–39

DOI 10.4171/RSMUP/127-2