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arXiv · 2406.00624

Iwasawa's main conjecture for Rankin-Selberg motives in the anticyclotomic case

Yifeng Liu·Yichao Tian·Liang Xiao
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Abstract

In this article, we study the Iwasawa theory for cuspidal automorphic representations of $\mathrm{GL}(n)\times\mathrm{GL}(n+1)$ over CM fields along anticyclotomic directions, in the framework of the Gan--Gross--Prasad conjecture for unitary groups. We prove one-side divisibility of the corresponding Iwasawa main conjecture: when the global root number is $1$, the $p$-adic $L$-function belongs to the characteristic ideal of the Iwasawa Bloch--Kato Selmer group; when the global root number is $-1$, the square of the characteristic ideal of a certain Iwasawa module is contained in the characteristic ideal of the torsion part of the Iwasawa Bloch--Kato Selmer group (analogous to Perrin-Riou's Heegner point main conjecture).

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Yifeng Liu, Yichao Tian, Liang Xiao. 2024-06-02. Iwasawa's main conjecture for Rankin-Selberg motives in the anticyclotomic case. https://arxiv.org/abs/2406.00624

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