### Tamely ramified extensions's structure.

Ibadula, Denis (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Ibadula, Denis (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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J. Carroll, H. Kisilevsky (1983)

Compositio Mathematica

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Martin J. Taylor (1980)

Annales de l'institut Fourier

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Let $E/F$ be a Galois extension of number fields with $\Gamma =$ Gal$(E/F)$ and with property that the divisors of $(E:F)$ are non-ramified in $E/\mathbf{Q}$. We denote the ring of integers of $E$ by ${\mathcal{O}}_{E}$ and we study ${\mathcal{O}}_{E}$ as a $\mathbf{Z}\Gamma $-module. In particular we show that the fourth power of the (locally free) class of ${\mathcal{O}}_{E}$ is the trivial class. To obtain this result we use Fröhlich’s description of class groups of modules and his representative for the class of ${\mathcal{E}}_{E}$, together with new determinantal congruences for cyclic group rings and corresponding...

John Coates (1980-1981)

Séminaire Bourbaki

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Kenkichi Iwasawa (1972)

Acta Arithmetica

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D. Burns (1991)

Journal de théorie des nombres de Bordeaux

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Let $L$ be a finite abelian extension of $\mathbb{Q}$, with ${\mathcal{O}}_{L}$ the ring of algebraic integers of $L$. We investigate the Galois structure of the unique fractional ${\mathcal{O}}_{L}$ -ideal which (if it exists) is unimodular with respect to the trace form of $L/\mathbb{Q}$.

Pollack, Robert, Weston, Tom (2007)

Documenta Mathematica

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Cornelius Greither (1992)

Annales de l'institut Fourier

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This first part of this paper gives a proof of the main conjecture of Iwasawa theory for abelian base fields, including the case $p=2$, by Kolyvagin’s method of Euler systems. On the way, one obtains a general result on local units modulo circular units. This is then used to deduce theorems on the order of $\chi $-parts of $p$-class groups of abelian number fields: first for relative class groups of real fields (again including the case $p=2$). As a consequence, a generalization of the Gras conjecture...