Control theorems for Selmer groups of nearly ordinary deformations

DOI10.1515/CRELLE.2011.120zbMath1248.11041MaRDI QIDQ2890364

Olivier Fouquet, Tadashi Ochiai

Publication date: 8 June 2012

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

zbMATH Keywords

Selmer groupsGalois representations\(p\)-adic representationcontrol theoremsIwasawa Main Conjecture

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (p)-adic theory, local fields (11F85) Galois representations (11F80) Zeta functions and (L)-functions of number fields (11R42) Iwasawa theory (11R23)

Related Items (9)

Deformations of Kolyvagin systems ⋮ Toric Periods and 𝑝-adic Families of Modular Forms of Half-Integral Weight ⋮ Purity for families of Galois representations ⋮ Main conjectures for higher rank nearly ordinary families. I ⋮ \(p\)-adic properties of motivic fundamental lines ⋮ Big Heegner point Kolyvagin system for a family of modular forms ⋮ Triple product \(p\)-adic \(L\)-functions for balanced weights ⋮ On primitive \(p\)-adic Rankin-Selberg \(L\)-functions ⋮ Triple product \(p\)-adic \(L\)-function attached to \(p\)-adic families of modular forms

Cites Work

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• Pseudo representations
• Nonvanishing theorems for automorphic \(L\)-functions on \(\text{GL} (2)\)
• Rational points of Abelian varieties with values in towers of number fields
• On the two-variable Iwasawa main conjecture
• Control theorem for Greenberg's Selmer groups of Galois deformations.

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