JournalsrsmupVol. 127pp. 17–39

The Arithmetic Theory of Local Constants for Abelian Varieties

  • Marco Adamo Seveso

    Università degli Studi di Milano, Italy
The Arithmetic Theory of Local Constants for Abelian Varieties cover
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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 ll be an odd rational prime and let L/KL/K be an abelian ll-power extension. Assume that we are given a quadratic extension K/kK/k such that L/kL/k is a dihedral extension and the abelian variety A/kA/k is defined over kk and polarizable. This theory can be used to relate the rank of the ll-Selmer group of AA over KK to the rank of the ll-Selmer group of AA over LL.

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