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arXiv · 2102.03421

Arithmetic local constants for abelian varieties with extra endomorphisms

Sunil Chetty
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Abstract

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 $\mathbb{Z}$. We then study the growth of the $p^\infty$-Selmer rank of our abelian variety, and we address the problem of extending the results of Mazur and Rubin to dihedral towers $k\subset K\subset F$ in which $[F:K]$ is not a $p$-power extension.

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Sunil Chetty. 2021-02-05. Arithmetic local constants for abelian varieties with extra endomorphisms. https://doi.org/10.7169/facm%2F2016.55.1.5

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