Algebraic aspects of Iwasawa theory in the Gan--Gross--Prasad setting

Abstract

This thesis sets up a framework to understand Iwasawa theory for the product of two unitary groups, generalizing phenomena observed in studying elliptic curves twisted by imaginary quadratic Hecke characters. The first part proves a formal theorem relating the different Iwasawa main conjectures arising in this picture. The second part interpolates the Selmer classes attached to the diagonal cycle appearing in the arithmetic Gan--Gross--Prasad conjecture. The final part is highly speculative and discusses the need for entirely new methods in the subject.