An Euler system for the adjoint of a modular form
Number Theory
2025-03-18 v2
Abstract
We construct an Euler system for the adjoint Galois representation of a modular form, using motivic cohomology classes arising from Hilbert modular surfaces. We use this Euler system to give an upper bound for the Selmer group of the adjoint representation over the cyclotomic Zp-extension, which agrees with the predictions of the Iwasawa main conjecture up to powers of p.
Cite
@article{arxiv.2312.04665,
title = {An Euler system for the adjoint of a modular form},
author = {David Loeffler and Sarah Livia Zerbes},
journal= {arXiv preprint arXiv:2312.04665},
year = {2025}
}
Comments
12 pages; revised to simplify the argument and obtain correct power of augmentation ideal