Computing isogeny classes of typical principally polarized abelian surfaces over the rationals
We describe an efficient algorithm which, given a principally polarized (pp) abelian surface
A over Q with geometric endomorphism ring equal to Z, computes all the other pp abelian …
A over Q with geometric endomorphism ring equal to Z, computes all the other pp abelian …
An effective open image theorem for products of principally polarized abelian varieties
J Mayle, T Wang - arXiv preprint arXiv:2212.11472, 2022 - arxiv.org
Let $ A=\prod_ {1\leq i\leq n} A_i $ be the product of principally polarized abelian varieties $
A_1,\ldots, A_n $, each defined over a number field $ K $, of a shared dimension $ g $, and …
A_1,\ldots, A_n $, each defined over a number field $ K $, of a shared dimension $ g $, and …
A uniform bound on the smallest surjective prime of an elliptic curve
Let $ E/\mathbb {Q} $ be an elliptic curve without complex multiplication. A well-known
theorem of Serre asserts that the $\ell $-adic Galois representation $\rho_ {E,\ell^\infty} $ is …
theorem of Serre asserts that the $\ell $-adic Galois representation $\rho_ {E,\ell^\infty} $ is …