On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights

2019/09/26 by Haining Wang, Wang, Haining · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1909.12374

openalex publication_date 2019/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study the Iwasawa theory for Hilbert modular forms over the anticyclotomic extension of a CM field. We prove a one sided divisibility result toward the Iwasawa main conjecture. The proof relies on the first and second reciprocity law relating theta elements to Heegner points Euler system. As a by-product we also prove certain Bloch-Kato type result in the rank 0 case and a parity conjecture

Citations

• On ordinary ?-adic representations associated to modular forms

Cited by

• Comparison of canonical periods under base change
• Quaternionic big Heegner points over totally real fields

Related

• Iwasawa Theory of Hilbert modular forms for anticyclotomic extension
• On Anticyclotomic Iwasawa Theory of Hecke Characters at Ordinary Primes
• Iwasawa theory for quadratic Hilbert modular forms
• Diagonal cycles and anticyclotomic Iwasawa theory of modular forms
• Anticyclotomic p-ordinary Iwasawa Theory of Elliptic Modular Forms