• DOI:10.1007/s00222-021-01088-4
• Corpus ID: 53959608

On the Beilinson–Bloch–Kato conjecture for Rankin–Selberg motives

@article{Liu2022OnTB,
  title={On the Beilinson–Bloch–Kato conjecture for Rankin–Selberg motives},
  author={Yifeng Liu and Yichao Tian and Liang Xiao and Wei Zhang and Xinwen Zhu},
  journal={Inventiones mathematicae},
  year={2022}
}

• Yifeng Liu, Yichao Tian, +2 authors Xinwen Zhu
• Published 26 December 2019
• Mathematics
• Inventiones mathematicae

In this article, we study the Beilinson-Bloch-Kato conjecture for motives corresponding to the Rankin-Selberg product 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 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.