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Étude d'un idéal particulier, d'indice fini dans le carré de l'idéal d'augmentation, associé à un caractère de Dirichlet d'un groupe fini

Hassan Oukhaba, Gilles Robert (1991)

Journal de théorie des nombres de Bordeaux

We describe here two sets of generators of an ideal Δ ( ψ ) = M ( ψ ) , of finite index inside the square I 2 of the augmentation ideal I of ℤ [ G ] , associated to the Dirichlet character ψ of the finite group G . That peculiar ideal first appeared in questions related to the computation of class number formulas for abelian non ramified extensions of 𝒜 -fields cf. [2] and [3], satisfying certain special conditions which are outlined in the introduction of [1]. A rough idea of these formulas is given in §§2 and 6.

Euclidean fields having a large Lenstra constant

Armin Leutbecher (1985)

Annales de l'institut Fourier

Based on a method of H. W. Lenstra Jr. in this note 143 new Euclidean number fields are given of degree n = 7 , 8 , 9 and 10 and of unit rank ≤ 5 . The search for these examples also revealed several other fields of small discriminant compared with the lower bounds of Odlyzko.

Euler system for Galois deformations

Tadashi Ochiai (2005)

Annales de l’institut Fourier

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 and the...

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