Iwasawa theory for the symmetric square of a modular form

TL;DR

This paper develops an Euler system for the symmetric square of a modular form, enabling bounds on associated Selmer groups and advancing understanding in Iwasawa theory for these Galois representations.

Contribution

It constructs a compatible family of global cohomology classes (Euler system) for the symmetric square of a modular form, a novel approach in this context.

Findings

Bounded Selmer groups of symmetric square Galois representations.

Established connections between Euler systems and Iwasawa theory.

Provided new tools for studying the arithmetic of modular forms.

Abstract

We construct a compatible family of global cohomology classes (an Euler system) for the symmetric square of a modular form, and apply this to bounding Selmer groups of the symmetric square Galois representation and its twists.