Displaying similar documents to “Iwasawa algebras and arithmetic”

The GL2 main conjecture for elliptic curves without complex multiplication

John Coates, Takako Fukaya, Kazuya Kato, Ramdorai Sujatha, Otmar Venjakob (2005)

Publications Mathématiques de l'IHÉS

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Let G be a compact -adic Lie group, with no element of order , and having a closed normal subgroup H such that G/H is isomorphic to . We prove the existence of a canonical Ore set S of non-zero divisors in the Iwasawa algebra Λ(G) of G, which seems to be particularly relevant for arithmetic applications. Using localization with respect to S, we are able to define a characteristic element for every finitely generated Λ(G)-module M which has the property that the quotient...

Euler system for Galois deformations

Tadashi Ochiai (2005)

Annales de l’institut Fourier

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In this paper, we develop the Euler system theory for Galois deformations. By applying this theory to the Beilinson-Kato Euler system for Hida’s nearly ordinary modular deformations, we prove one of the inequalities predicted by the two-variable Iwasawa main conjecture. Our method of the proof of the Euler system theory is based on non-arithmetic specializations. This gives a new simplified proof of the inequality between the characteristic ideal of the Selmer group of a Galois deformation...