Results 121 to 130 of about 14,098 (157)
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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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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.
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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.
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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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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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Iwasawa’s Theory of ℤ-extensions
1997The theory of ℤ p -extensions has turned out to be one of the most fruitful areas of research in number theory in recent years. The subject receives its motivation from the theory of curves over finite fields, which is known to have a strong analogy with the theory of number fields.
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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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Iwasawa Theory of Shimura Varieties
This paper provides a comprehensive survey of the Iwasawa theory of Shimura varieties, a central topic in modern number theory that synthesizes arithmetic algebraic geometry, automorphic forms, and Galois representations. We explore the historical development of both Iwasawa theory, initiated by Kenkichi Iwasawa's work on ideal class groups in ...openaire +1 more source