A weak form of Greenberg's conjecture for the cyclotomic ℤ₂-extension of real quadratic fields

2024/12/16 by Naoki Kumakawa
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems

paper · doi:10.7169/facm/240331-2-9

Abstract

In this paper, we show that a weak form of Greenberg's conjecture for the cyclotomic ℤ₂-extension of ℚ(√(p)) is true, where p is an odd prime number satisfying certain arithmetic conditions. As an application, we obtain an upper bound of the Iwasawa λ-invariant of the cyclotomic ℤ₂-extension of ℚ(√(p)) under some additional conditions on ℚ(√(p)).

Related

• Iwasawa module of the cyclotomic ℤ₂-extension of certain real quadratic fields
• Greenberg's conjecture for real quadratic fields and the cyclotomic ℤ₂-extensions
• ℤ₂-extension of real quadratic fields with ℤ/2ℤ as 2-class group at each layer
• Weak Greenberg's generalized conjecture for imaginary quadratic fields
• Greenberg's conjecture and cyclotomic towers