Results 101 to 110 of about 292 (134)
Some of the next articles are maybe not open access.
On the Role of the Points at Infinity in Iwasawa Theory
American Journal of Mathematics, 1987This article is devoted to some aspects of the algebraic theory of cyclotomic \({\mathbb{Z}}_ p\)-fields \(K=k(\mu_{p^{\infty}})\). The author uses Iwasawa's theory of sheaves for algebraic number fields [\textit{K. Iwasawa}, Ann. Math., II. Ser. 69, 408-413 (1959; Zbl 0090.029)] in order to improve some classical results, and to poke at Greenberg's ...
openaire +2 more sources
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
openaire +3 more sources
2006
AbstractThis chapter proves the torsion of the anticyclotomic Iwasawa module of a (p-ordinary) CM field, and presents an explicit formula of the L-invariant of the CM field, which is a natural generalization of the formula by Ferrero-Greenberg and Gross-Koblitz from the 1970s for imaginary quadratic fields.
openaire +1 more source
AbstractThis chapter proves the torsion of the anticyclotomic Iwasawa module of a (p-ordinary) CM field, and presents an explicit formula of the L-invariant of the CM field, which is a natural generalization of the formula by Ferrero-Greenberg and Gross-Koblitz from the 1970s for imaginary quadratic fields.
openaire +1 more source
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 his election as FRS’.
openaire +3 more sources
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
openaire +1 more source
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
openaire +1 more source
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.
openaire +1 more source
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 ...
openaire +1 more source
Higher codimension Iwasawa theory for elliptic curves with supersingular reduction
Annales Mathematiques Du Quebec, 2023Takenori Kataoka
exaly