Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593860 | Journal of Number Theory | 2013 | 13 Pages |
Abstract
Using a multi-dimensional large sieve inequality, we prove that, for almost all pairs (or indeed almost all k-tuples) of elliptic curves, the associated Galois representation on their torsion has maximal image. This generalizes the authorʼs previous work and provides evidence for an affirmative answer to a higher-dimensional analogue of Serreʼs uniformity question for single elliptic curves. Furthermore, as a consequence of our main theorem, one deduces the triviality of the Brauer group of the Kummer surface attached to almost all pairs of elliptic curves.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Nathan Jones,