Rendiconti del Seminario Matematico della Università di Padova
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Published online: 2012-12-17
The Arithmetic Theory of Local Constants for Abelian VarietiesMarco Adamo Seveso (1) Università degli Studi di Milano, Italy
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 $l$ be an oddrational prime and let $L/K$ be an abelian $l$-power extension. Assume that weare given a quadratic extension $K/k$ such that $L/k$ is a dihedral extensionand the abelian variety $A/k$ is defined over $k$ and polarizable. This theorycan be used to relate the rank of the $l$-Selmer group of $A$ over $K$ to the rankof the $l$-Selmer group of $A$ over $L$.
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Seveso Marco Adamo: The Arithmetic Theory of Local Constants for Abelian Varieties. Rend. Sem. Mat. Univ. Padova 127 (2012), 17-39. doi: 10.4171/RSMUP/127-2