On the Beilinson–Bloch–Kato conjecture for Rankin–Selberg motives
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222_2021_1088_ReferencePDF.pdf
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Author(s)
Liu, Yifeng
Tian, Yichao
Xiao, Liang
Zhang, Wei
Zhu, Xinwen
Date Issued
January 21, 2022
Publisher
Springer Berlin Heidelberg
Citation
Liu, Yifeng, Tian, Yichao, Xiao, Liang, Zhang, Wei and Zhu, Xinwen. 2022. "On the Beilinson–Bloch–Kato conjecture for Rankin–Selberg motives."
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Author's final manuscript
Abstract
Abstract
In this article, we study the Beilinson–Bloch–Kato conjecture for motives associated to Rankin–Selberg products of conjugate self-dual automorphic representations, within the framework of the Gan–Gross–Prasad conjecture. We show that if the central critical value of the Rankin–Selberg L-function does not vanish, then the Bloch–Kato Selmer group with coefficients in a favorable field of the corresponding motive vanishes. We also show that if the class in the Bloch–Kato Selmer group constructed from a certain diagonal cycle does not vanish, which is conjecturally equivalent to the nonvanishing of the central critical first derivative of the Rankin–Selberg L-function, then the Bloch–Kato Selmer group is of rank one.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00222-021-01088-4
