Beilinson-Flach elements and Euler systems I: Syntomic regulators and 𝑝-adic Rankin 𝐿-series

Bertolini, Massimo; Darmon, Henri; Rotger, Victor

doi:10.1090/S1056-3911-2014-00670-6

Beilinson-Flach elements and Euler systems I: Syntomic regulators and $p$-adic Rankin $L$-series

Authors: Massimo Bertolini, Henri Darmon and Victor Rotger
Journal: J. Algebraic Geom. 24 (2015), 355-378
DOI: https://doi.org/10.1090/S1056-3911-2014-00670-6
Published electronically: December 18, 2014
MathSciNet review: 3311587
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Abstract | References | Additional Information

Abstract: This article is the first in a series devoted to the Euler system arising from $p$-adic families of Beilinson-Flach elements in the first $K$-group of the product of two modular curves. It relates the image of these elements under the $p$-adic syntomic regulator (as described by Besser (2012)) to the special values at the near-central point of Hida’s $p$-adic Rankin $L$-function attached to two Hida families of cusp forms.

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Additional Information

Massimo Bertolini
Affiliation: Universität Duisburg-Essen, Fakultät für Mathematik, Mathematikcarrée, Thea-Leymann-Strasse 9, 45326 Essen, Germany
MR Author ID: 249679
Email: massimo.bertolini@uni-due.de

Henri Darmon
Affiliation: McGill University, Burnside Hall, Room 1111, Montréal, Quebec H3A 0G4, Canada
MR Author ID: 271251
Email: darmon@math.mcgill.ca

Victor Rotger
Affiliation: Universitat Politècnica de Catalunya, MA II, Despatx 413, C. Jordi Girona 1-3, 08034 Barcelona, Spain
MR Author ID: 698263
Email: victor.rotger@upc.edu

Received by editor(s): June 21, 2012
Received by editor(s) in revised form: August 20, 2014, October 24, 2014, and October 29, 2014
Published electronically: December 18, 2014
Additional Notes: During the preparation of this work, the first author was financially supported by MIUR-Prin, the second author by an NSERC Discovery grant, and the third author by MTM20121-34611
Article copyright: © Copyright 2014 University Press, Inc.