2018/03/22 by Myungjun Yu · 3 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research
paper · pdf · doi:10.1090/tran/7563
Let E and A be elliptic curves over a number field K. Let χ be a quadratic character of K. We prove the conjecture posed by Mazur and Rubin on n-Selmer near-companion curves in the case n=2. Namely, we show if the difference of the 2-Selmer ranks of Eχ and Aχ is bounded independent of χ, there is a GK-module isomorphism E[2] ≅ A[2].