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arXiv · 2204.07658

An anticyclotomic Euler system for adjoint modular Galois representations

Raúl Alonso·Francesc Castella·Óscar Rivero
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Abstract

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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Raúl Alonso, Francesc Castella, Óscar Rivero. 2022-04-15. An anticyclotomic Euler system for adjoint modular Galois representations. https://arxiv.org/abs/2204.07658

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