This work generalizes the theory of arithmetic local constants, introduced by Mazur and Rubin, to better address abelian varieties with a larger endomorphism ring than ℤ. We then study the growth of the p∞- Selmer rank of our abelian variety, and we address the problem of extending the results of Mazur and Rubin to dihedral towers k ⊂ K ⊂ F in which [F : K] is not a p-power extension.
This is a pre-print of an article accepted for publication in Functiones et Approximatio, Commentarii Mathematici. ©2016.
Chetty S. 2016. Arithmetic local constants for abelian varieties with extra endomorphisms. Accepted for publication in Functiones et Approximatio, Commentarii Mathematici.