Survey on bounding Selmer groups for Rankin--Selberg motives

2025/09/21 by Yifeng Liu, Yichao Tian, Liu, Yifeng +7
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2509.16881

openalex publication_date 2025/09/21 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

This article reviews the work of the same authors on the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives, with some new observations and speculations toward the categorical local Langlands developed by X. Zhu.

Citations

• On the generic part of the cohomology of Shimura varieties of abelian type
• On Ihara's lemma for definite unitary groups
• Iwasawa's main conjecture for Rankin-Selberg motives in the anticyclotomic case
• Deformation of rigid conjugate self-dual Galois representations
• Coherent sheaves on the stack of Langlands parameters
• On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives
• Symmetric power functoriality for holomorphic modular forms
• Isolation of cuspidal spectrum, with application to the Gan--Gross--Prasad conjecture
• On the generic part of the cohomology of non-compact unitary Shimura varieties
• Cycles on Shimura varieties via geometric Satake
• Bounding cubic-triple product Selmer groups of elliptic curves
• The conjectural connections between automorphic representations and Galois representations
• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Propri�t�s galoisiennes des points d'ordre fini des courbes elliptiques

Related

• On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives
• On the Beilinson-Bloch-Kato conjecture for polarized motives
• Functional equations for multi-signed Selmer groups
• Iwasawa's main conjecture for Rankin-Selberg motives in the anticyclotomic case
• The refined Tamagawa number conjectures for GL₂