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Iwasawa's main conjecture for Rankin-Selberg motives in the anticyclotomic case
- Publication Year :
- 2024
-
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).<br />Comment: 105 pages; main theorems improved; comments welcome. arXiv admin note: text overlap with arXiv:2211.06673 by other authors
- Subjects :
- Mathematics - Number Theory
11G05, 11G18, 11G40, 11R34
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2406.00624
- Document Type :
- Working Paper