Arithmetic Geometry and Number Theory RTG Seminar: Bounding 5-torsion in class groups using Elliptic Curves

Seminar | March 18 | 3-5 p.m. | 748 Evans Hall

 Jacob Tsimerman, University of Toronto

 Department of Mathematics

We discuss a new method to bound 5-torsion in class groups using elliptic curves. The most natural “trivial” bound on the n-torsion is to bound it by the size of the entire class group, for which one has a global class number formula. We explain how to make sense of the n-torsion of a class group intrinsically as a “dimension 0 selmer group”, and by embedding it into an appropriate Elliptic curve we can bound its size by the Tate-Shafarevich group which we can bound using the BSD conjecture. This fits into a general paradigm where one bounds “dimension 0 selmer groups” by embedding into global objects, and using class number formulas. (joint with Arul Shankar)