\(p^r\)-Selmer companion modular forms

DOI10.5802/aif.3392zbMath1472.11132arXiv1806.04944OpenAlexW3156397606MaRDI QIDQ2034708

Dipramit Majumdar, Somnath Jha, Sudhanshu Shekhar

Publication date: 22 June 2021

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.04944

zbMATH Keywords

congruence of modular formsresidual Bloch-Kato Selmer group

Mathematics Subject Classification ID

Galois cohomology (11S25) Congruences for modular and (p)-adic modular forms (11F33) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23) Galois cohomology (11R34)

Uses Software

• SageMath
• LMFDB

Cites Work

• Coleman maps and the \(p\)-adic regulator
• Variation of Iwasawa invariants in Hida families
• On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
• On ordinary \(\lambda\)-adic representations associated to modular forms
• On the conductors of mod \(\ell\) Galois representations coming from modular forms
• Iwasawa theory for elliptic curves at supersingular primes
• Control theorem for Bloch-Kato's Selmer groups of \(p\)-adic representations
• Motives for modular forms
• Canonical periods and congruence formulae
• Arithmetic properties of signed Selmer groups at non-ordinary primes
• The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
• Iwasawa theory for modular forms at supersingular primes
• Visualizing Elements in the Shafarevich—Tate Group
• On the Asymptotic Growth of Bloch-Kato-Shafarevich-Tate Groups of Modular Forms Over Cyclotomic Extensions
• Selmer companion curves
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