Anticyclotomic main conjecture and the non-triviality of Rankin-Selberg \(L\)-values in Hida families

DOI10.1016/j.jnt.2023.03.007zbMath1528.11115arXiv2205.08081WikidataQ123024432 ScholiaQ123024432MaRDI QIDQ6101543

Chan-Ho Kim, Matteo Longo

Publication date: 1 June 2023

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.08081

zbMATH Keywords

Iwasawa theoryHida familiescontrol theoremanticyclotomic main conjectureRankin-Selberg \(L\)-values

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Iwasawa theory (11R23)

Related Items (1)

An explicit comparison of anticyclotomic p-adic L-functions for Hida families

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Big Heegner points and special values of \(L\)-series
• Quaternion algebras, Heegner points and the arithmetic of Hida families
• Iwasawa's main conjecture for elliptic curves over anticyclotonic \(\mathbb Z_p\)-extensions
• Variation of Heegner points in Hida families
• Galois representations into \(\text{GL}_2(\mathbb Z_pX)\) attached to ordinary cusp forms.
• Control theorem for Bloch-Kato's Selmer groups of \(p\)-adic representations
• Variation of anticyclotomic Iwasawa invariants in Hida families
• \(p\)-adic \(L\)-functions and \(p\)-adic periods of modular forms
• The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
• Vanishing of special values and central derivatives in Hida families
• A refined Beilinson–Bloch conjecture for motives of modular forms
• On the two-variable Iwasawa main conjecture
• Control theorem for Greenberg's Selmer groups of Galois deformations.
• Heegner points on Mumford-Tate curves

This page was built for publication: Anticyclotomic main conjecture and the non-triviality of Rankin-Selberg \(L\)-values in Hida families