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Eisenstein congruences among Euler systems

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  06 November 2023

Ó. Rivero Open the ORCID record for Ó. Rivero [Opens in a new window]  and
V. Rotger
Ó. Rivero*
Affiliation:
Simons Laufer Mathematical Sciences Institute, 17 Gauss Way, Berkeley, CA 94720, United States
V. Rotger
Affiliation:
IMTech, UPC and Centre de Recerca Matemàtiques, C. Jordi Girona 1-3, 08034 Barcelona, Spain e-mail: victor.rotger@upc.edu
*
e-mail: riverosalgado@gmail.com
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Abstract

We investigate Eisenstein congruences between the so-called Euler systems of Garrett–Rankin–Selberg type. This includes the cohomology classes of Beilinson–Kato, Beilinson–Flach, and diagonal cycles. The proofs crucially rely on different known versions of the Bloch–Kato conjecture, and are based on the study of the Perrin-Riou formalism and the comparison between the different p-adic L-functions.

Keywords

Eisenstein seriescongruencesEuler systemsp-adic L-functionsArtin formalism

MSC classification

Primary: 11F33: Congruences for modular and $p$-adic modular forms
Secondary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 11F80: Galois representations
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 22
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 682152). Ó.R. was further supported by the Royal Society Newton International Fellowship (Grant No. NIF$\backslash$R1$\backslash$202208). V.R. is supported by Icrea through an Icrea Academia Grant. This material is based upon work supported by the National Science Foundation under Grant No. DMS-1928930 while Ó.R. was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2023 semester.

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