Abstract
We study weight one specializations of the Euler system of Beilinson–Flach elements introduced by Kings, Loeffler and Zerbes, with a view towards a conjecture of Darmon, Lauder and Rotger relating logarithms of units in suitable number fields to special values of the Hida–Rankin p-adic L-function. We show that the latter conjecture follows from expected properties of Beilinson–Flach elements and prove the analogue of the main theorem of Castella and Hsieh about generalized Kato classes.
Funding source: Ministerio de Economía y Competitividad
Award Identifier / Grant number: MTM2015-63829-P
Funding source: H2020 European Research Council
Award Identifier / Grant number: 682152
Funding source: “la Caixa” Foundation
Award Identifier / Grant number: LCF/BQ/ES17/11600010
Funding statement: Both authors were supported by grant MTM2015-63829-P. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 682152). The first author has also received financial support through “la Caixa” Fellowship Grant for Doctoral Studies (grant LCF/BQ/ES17/11600010).
Acknowledgements
We sincerely thank the anonymous referees, whose comments notably contributed to improve the exposition of this note.
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