MATH Seminar

Title: Torsion in Odd Degree
Seminar: Algebra
Speaker: Abbey Bourdon of University of Georgia
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2015-12-01 at 4:00PM
Venue: W304
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Abstract: Let E be an elliptic curve defined over a number field F. It is a classical theorem of Mordell and Weil that the collection of points of E with coordinates in F form a finitely generated abelian group. We seek to understand the subgroup of points with finite order. In particular, given a positive integer d, we would like to know precisely which abelian groups arise as the torsion subgroup of an elliptic curve defined over a number field of degree d. I will discuss recent progress on this problem for the special class of elliptic curves with complex multiplication (CM). In particular, if d is odd, we now have a complete classification of the groups that arise as the torsion subgroup of a CM elliptic curve defined over a number field of degree d. This is joint work with Paul Pollack.