Title: The growth of the Bloch-Kato-Shafarevich-Tate group for modular forms
Speaker: Florian Sprung
Speaker Info: Princeton University
Brief Description:
Special Note:
Abstract:
The Bloch-Kato-Shafarevich-Tate group for modular forms is an analogue of the class group for number fields. Like the class group, it is hard to compute the size of this group. In the 1950's, Iwasawa invented a method to shed light on the size of the class group in an infinite tower of number fields. In this talk, we establish similar formulas for modular forms. These formulas traditionally include another term (the Kurihara term), which our formulas do, too. However, when the weight of the form is large enough, there is a new term that hasn't appeared anywhere yet. This is based on joint work with Rei Otsuki. If time permits, we will (literally) sketch a surprising phenomenon about these formulas.Date: Monday, April 24, 2017