Open Access
September 2016 Arithmetic local constants for abelian varieties with extra endomorphisms
Sunil Chetty
Funct. Approx. Comment. Math. 55(1): 59-81 (September 2016). DOI: 10.7169/facm/2016.55.1.5


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.


Download Citation

Sunil Chetty. "Arithmetic local constants for abelian varieties with extra endomorphisms." Funct. Approx. Comment. Math. 55 (1) 59 - 81, September 2016.


Published: September 2016
First available in Project Euclid: 19 September 2016

zbMATH: 06862553
MathSciNet: MR3549013
Digital Object Identifier: 10.7169/facm/2016.55.1.5

Primary: 11G05 , 11G10
Secondary: 11G07 , 11G15

Keywords: abelian variety , Complex Multiplication , Elliptic curve , Selmer rank

Rights: Copyright © 2016 Adam Mickiewicz University

Vol.55 • No. 1 • September 2016
Back to Top