On the Beilinson-Bloch-Kato conjecture for polarized motives

Hao Peng

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arXiv · 2509.18615

On the Beilinson-Bloch-Kato conjecture for polarized motives

Hao Peng

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Abstract

We study the Beilinson-Bloch-Kato conjecture for polarized motives. In the conjugate self-dual case, we show that if the central $L$-value does not vanish, then the associated Bloch-Kato Selmer group with coefficients in a suitable local field vanishes. In the self-dual analytic rank-zero case, we reduce the conjecture to a conjecture in the endoscopic Rankin-Selberg case related to the orthogonal Gross-Prasad periods.

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Hao Peng. 2025-09-23. On the Beilinson-Bloch-Kato conjecture for polarized motives. https://arxiv.org/abs/2509.18615

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