An Euler system for the adjoint of a modular form

2023/12/07 by Loeffler, David, Zerbes, Sarah Livia
#11F67 11F80 11G18 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2312.04665

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.

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