Uniform irreducibility of Galois action on the $\ell$-primary part of Abelian $3$-folds of Picard type

Fuente: arXiv
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Main Authors: Dimitrov, Mladen, Ramakrishnan, Dinakar
Format: Preprint
Published: 2025
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author Dimitrov, Mladen
Ramakrishnan, Dinakar
author_facet Dimitrov, Mladen
Ramakrishnan, Dinakar
contents Half a century ago Manin showed that given a number field $k$ and a rational prime $\ell$, there exists a uniform bound for the order of cyclic $\ell$-power isogenies between two non-CM elliptic curves over $k$. We generalize this to certain $2$-dimensional families of abelian $3$-folds with multiplication by an imaginary quadratic field.
format Preprint
id arxiv_https___arxiv_org_abs_2511_04609
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Uniform irreducibility of Galois action on the $\ell$-primary part of Abelian $3$-folds of Picard type
Dimitrov, Mladen
Ramakrishnan, Dinakar
Number Theory
Algebraic Geometry
Representation Theory
11G18, 14G35, 14G05, 11F70
Half a century ago Manin showed that given a number field $k$ and a rational prime $\ell$, there exists a uniform bound for the order of cyclic $\ell$-power isogenies between two non-CM elliptic curves over $k$. We generalize this to certain $2$-dimensional families of abelian $3$-folds with multiplication by an imaginary quadratic field.
title Uniform irreducibility of Galois action on the $\ell$-primary part of Abelian $3$-folds of Picard type
topic Number Theory
Algebraic Geometry
Representation Theory
11G18, 14G35, 14G05, 11F70
url https://arxiv.org/abs/2511.04609