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Bimodules and Abelian Surfaces
- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms/bdv097
- Publisher site
- See Article on Publisher Site
Abstract
Let p and q be distinct primes. Consider the Shimura curve Xpq associated to the indefinite quaternion algebra of discriminant pq over Q. Let Jpq be the Jacobian variety of Xpq, which is an abelian variety over Q. For an odd prime ℓ, we provide sufficient conditions for the non‐existence of rational points of order ℓ on Jpq. As an application, we find some non‐trivial subgroups of the kernel of an isogeny from the new quotient J0(pq)new of J0(pq) to Jpq.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Feb 1, 2016