Functiones et Approximatio Commentarii Mathematici

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.

Article information

Source
Funct. Approx. Comment. Math. Volume 55, Number 1 (2016), 59-81.

Dates
First available in Project Euclid: 19 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.facm/1474301230

Digital Object Identifier
doi:10.7169/facm/2016.55.1.5

Mathematical Reviews number (MathSciNet)
MR3549013

Subjects
Primary: 11G05: Elliptic curves over global fields [See also 14H52] 11G10: Abelian varieties of dimension > 1 [See also 14Kxx]
Secondary: 11G07: Elliptic curves over local fields [See also 14G20, 14H52] 11G15: Complex multiplication and moduli of abelian varieties [See also 14K22]

Keywords
elliptic curve abelian variety Selmer rank complex multiplication

Citation

Chetty, Sunil. Arithmetic local constants for abelian varieties with extra endomorphisms. Funct. Approx. Comment. Math. 55 (2016), no. 1, 59--81. doi:10.7169/facm/2016.55.1.5. https://projecteuclid.org/euclid.facm/1474301230.


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