Iwasawa theory of Hilbert modular forms for anticyclotomic extensions without Ihara's lemma

DOI10.5565/publmat6812403arXiv1909.10162OpenAlexW4390008299WikidataQ124964385 ScholiaQ124964385MaRDI QIDQ6146756

Bing Yong Xie

Publication date: 15 January 2024

Published in: Publicacions Matemàtiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.10162

zbMATH Keywords

anticyclotomic extensionsSelmer groups\(p\)-adic \(L\)-functionsIwasawa main conjecture

Mathematics Subject Classification ID

Iwasawa theory (11R23)

Cites Work

• Anticyclotomic Iwasawa's main conjecture for Hilbert modular forms
• Gross-Zagier formula for \(\text{GL}_ 2\).
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• On Galois representations associated to Hilbert modular forms
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• Level lowering for modular \(\text{mod }\ell\) representations over totally real fields
• Non-optimal levels of \(\text{mod }l\) modular representations
• Special values of anticyclotomic \(L\)-functions for modular forms
• A simple proof of Langlands conjectures for \(\text{GL}_n\) on a \(p\)-adic field
• Ihara's lemma for Shimura curves over totally real fields via patching
• Level Raising and Anticyclotomic Selmer Groups for Hilbert Modular Forms of Weight Two
• On anticyclotomic μ-invariants of modular forms
• Néron Models
• Sur les représentations $l$-adiques associées aux formes modulaires de Hilbert
• Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms
• On the anticyclotomic Iwasawa main conjecture for modular forms
• On the freeness of anticyclotomic Selmer groups of modular forms

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