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An anticyclotomic Euler system for adjoint modular Galois representations

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Title: An anticyclotomic Euler system for adjoint modular Galois representations
Authors: Alonso, Raúl, Castella, Francesc, Rivero, Óscar
Source: Annales de l'Institut Fourier. 75:291-329
Publication Status: Preprint
Publisher Information: Cellule MathDoc/Centre Mersenne, 2025.
Publication Year: 2025
Subject Terms: Mathematics - Number Theory, 11R23 (Primary) 11F85, 14G35 (Secondary), FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, 01 natural sciences
Description: Let K be an imaginary quadratic field and p a prime split in K. In this paper we construct an anticyclotomic Euler system for the adjoint representation attached to elliptic modular forms base changed to K. We also relate our Euler system to a p-adic L-function deduced from the construction by Eischen–Wan and Eischen–Harris–Li–Skinner of p-adic L-functions for unitary groups. This allows us to derive new cases of the Bloch–Kato conjecture in rank zero, and a divisibility towards an Iwasawa main conjecture.
Document Type: Article
Language: English
ISSN: 1777-5310
DOI: 10.5802/aif.3646
DOI: 10.48550/arxiv.2204.07658
Access URL: http://arxiv.org/abs/2204.07658
Rights: CC BY
Accession Number: edsair.doi.dedup.....1b64a6ad4bf4197ec901b6fcc06e52a0
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  Data: An anticyclotomic Euler system for adjoint modular Galois representations
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  Data: <searchLink fieldCode="AR" term="%22Alonso%2C+Raúl%22">Alonso, Raúl</searchLink><br /><searchLink fieldCode="AR" term="%22Castella%2C+Francesc%22">Castella, Francesc</searchLink><br /><searchLink fieldCode="AR" term="%22Rivero%2C+Óscar%22">Rivero, Óscar</searchLink>
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  Data: <i>Annales de l'Institut Fourier</i>. 75:291-329
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  Data: Preprint
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  Data: Cellule MathDoc/Centre Mersenne, 2025.
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  Data: Let K be an imaginary quadratic field and p a prime split in K. In this paper we construct an anticyclotomic Euler system for the adjoint representation attached to elliptic modular forms base changed to K. We also relate our Euler system to a p-adic L-function deduced from the construction by Eischen–Wan and Eischen–Harris–Li–Skinner of p-adic L-functions for unitary groups. This allows us to derive new cases of the Bloch–Kato conjecture in rank zero, and a divisibility towards an Iwasawa main conjecture.
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  Data: 10.5802/aif.3646
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  Data: 10.48550/arxiv.2204.07658
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