Uniform irreducibility of Galois action on the $\ell$-primary part of Abelian $3$-folds of Picard type
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912928359251968 |
|---|---|
| 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 |