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math.NT2017★ 6 cited
Hyperelliptic Curves with Maximal Galois Action on the Torsion Points of their Jacobians
Aaron Landesman, Ashvin Swaminathan, James Tao +1
In this article, we show that in each of four standard families of hyperelliptic curves, there is a density- subset of members with the property that their Jacobians have adelic…
math.NT2016★ 16 cited
Surjectivity of Galois Representations in Rational Families of Abelian Varieties
Aaron Landesman, Ashvin Swaminathan, James Tao +1
In this article, we show that for any non-isotrivial family of abelian varieties over a rational base with big monodromy, those members that have adelic Galois representation with…