2026/07/16 by Alexander Galarraga
Mathematics · #math.NT #math.AG
A curve over a number field has infinitely many degree-d points if and only if there exists a degree-d ℙ1- or AV-parametrized point. We show that a ℙ1-isolated AV-parametrized point arises only from an abelian translate satisfying a certain property, which we term ``indecomposable". We apply our results to a family of genus-7 curves for which we can show that every effective abelian translate in degree 5 is decomposable over the algebraic closure, giving a negative answer to a question of Viray and Vogt.