2019/06/20 by Netan Dogra, Dogra, Netan, Samuel Le Fourn +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1906.08751
openalex publication_date 2019/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we provide refined sufficient conditions for the quadratic Chabauty method to produce a finite set of points, with the conditions on the rank of the Jacobian replaced by conditions on the rank of a quotient of the Jacobian plus an associated space of Chow-Heegner points. We then apply this condition to prove the finiteness of this set for any modular curves Xns + (N) and X0 + (N) of genus at least 2 with N prime. The proof relies on the existence of a quotient of their Jacobians whose Mordell-Weil rank is equal to its dimension (and at least 2), which is proven via analytic estimates for orders of vanishing of L-functions of modular forms, thanks to a Kolyvagin-Logachev type result.