An Euler system for the adjoint of a modular form

David Loeffler; Sarah Livia Zerbes

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arXiv · 2312.04665

An Euler system for the adjoint of a modular form

David Loeffler·Sarah Livia Zerbes

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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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David Loeffler, Sarah Livia Zerbes. 2023-12-07. An Euler system for the adjoint of a modular form. https://arxiv.org/abs/2312.04665

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