MATH Seminar

Title: Torsion subgroups of rational elliptic curves over the compositum of all cubic fields.
Seminar: Algebra
Speaker: Drew Sutherland of MIT
Contact: David Zureick-Brown, dab@mathcs.emory.edu
Date: 2016-03-18 at 4:00PM
Venue: MSC W303
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Abstract: Let E/Q be an elliptic curve and let Q(3^infty) denote the compositum of all cubic extensions of Q. While the group E(3^infty) is not finitely generated, one can show that its torsion subgroup is finite; this holds more generally for any Galois extension of Q that contains only finitely many roots of unity. I will describe joint work with Daniels, Lozano-Robledo, and Najman, in which we obtain a complete classification of the 20 torsion subgroups that can and do occur, along with an explicit description of the elliptic curves E/Q that realize each possibility (up to twists). This is achieved by determining the rational points on a corresponding set of modular curves and relies on several recent results related to the mod-n Galois representations attached to elliptic curves over Q.