Results 111 to 120 of about 302 (145)
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Selmer groups in Iwasawa theory and congruences
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2019This article outlines the behaviour of Iwasawa μ -invariants for Selmer groups of elliptic curves when the residual representations are equivalent. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of ...
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Iwasawa Theory of Number Fields
2008As shown in the previous chapters, there is a remarkable analogy between the theory of algebraic number fields and the theory of function fields in one variable over a finite field. This analogy should also extend to the theory of ζ-functions and L-functions of global fields. If, for a function field k, one considers the corresponding smooth and proper
Jürgen Neukirch +2 more
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On capitulation cokernels in Iwasawa theory
American Journal of Mathematics, 2005For a number field F and an odd prime p , we study the "capitulation cokernels" coker ( A ' n → A ' Γ n ∞ ) associated with the ( p )-class groups of the cyclotomic [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]-extension of F .
Movahhedi, Abbas C. +2 more
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Iwasawa theory and Fitting ideals
Journal für die reine und angewandte Mathematik (Crelles Journal), 2003Let \(F/{\mathbb Q}\) be an imaginary abelain extension of finite degree and let \(\text{Cl}'(F)\) denote the class group of \(F\) considered over the ring \({\mathbb Z}':={\mathbb Z}[1/2]\), so that it is viewed as a \({\mathbb Z}'[\text{Gal}(F/{\mathbb Q}]\)-module. For any module \(M\) over this group ring, \(M^-\) denotes the submodule on which the
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Quadratic Exercises in Iwasawa Theory
International Mathematics Research Notices, 2008The anticyclotomic main conjecture for CM fields was proven in 2006 under some restrictive conditions. In this paper, we remove the assumption on the conductor of the blanch character, and therefore, the conjecture is now proven to be true under very mild conditions.
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Completed cohomology and Iwasawa theory
2019We compare two different constructions of cyclotomic p-adic L-functions for modular forms and their relationship to Galois cohomology: one using Kato's Euler system and the other using Emerton's p-adically completed cohomology of modular curves. At a more technical level, we prove the equality of two elements of a local Iwasawa cohomology group, one ...
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1978
Iwasawa [Iw 8], [Iw 10] developed a theory of local units analogous to the global theory, taking projective limits, especially in the cyclotomic tower, and getting the structure of this projective limit modulo the closure of the cyclotomic units. He considers eigenspaces for the characters of Gal(K0/Q p ) where K0 = Q p (ζ) with a primitive pth root of
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Iwasawa [Iw 8], [Iw 10] developed a theory of local units analogous to the global theory, taking projective limits, especially in the cyclotomic tower, and getting the structure of this projective limit modulo the closure of the cyclotomic units. He considers eigenspaces for the characters of Gal(K0/Q p ) where K0 = Q p (ζ) with a primitive pth root of
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Arithmetic statistics for the fine Selmer group in Iwasawa theory
Research in Number Theory, 2023Anwesh Ray, Sujatha R
exaly
Topics in anticyclotomic Iwasawa theory
Let p ≥ 5 be a prime and E/ℚ be an elliptic curve of conductor N that is ordinary at p. Let K/ℚ be an imaginary quadratic field. This thesis is concerned with the dual Selmer group of E over the anticyclotomic extension of K, especially when p is split in K and K satisfies the Heegner hypothesis for E: every prime ℓ dividing N is split in K/ℚ.openaire +1 more source