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An anticyclotomic Euler system for adjoint modular Galois representations

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Název:	An anticyclotomic Euler system for adjoint modular Galois representations
Autoři:	Alonso, Raúl, Castella, Francesc, Rivero, Óscar
Zdroj:	Annales de l'Institut Fourier. 75:291-329
Publication Status:	Preprint
Informace o vydavateli:	Cellule MathDoc/Centre Mersenne, 2025.
Rok vydání:	2025
Témata:	Mathematics - Number Theory, 11R23 (Primary) 11F85, 14G35 (Secondary), FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, 01 natural sciences
Popis:	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.
Druh dokumentu:	Article
Jazyk:	English
ISSN:	1777-5310
DOI:	10.5802/aif.3646
DOI:	10.48550/arxiv.2204.07658
Přístupová URL adresa:	http://arxiv.org/abs/2204.07658
Rights:	CC BY
Přístupové číslo:	edsair.doi.dedup.....1b64a6ad4bf4197ec901b6fcc06e52a0
Databáze:	OpenAIRE

Popis
Abstrakt:	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.
ISSN:	17775310
DOI:	10.5802/aif.3646