Displaying similar documents to “On Iwasawa’s λ-invariant for certain Z l -extensions”

Galois module structure of rings of integers

Martin J. Taylor (1980)

Annales de l'institut Fourier

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Let E / F be a Galois extension of number fields with Γ = Gal ( E / F ) and with property that the divisors of ( E : F ) are non-ramified in E / Q . We denote the ring of integers of E by 𝒪 E and we study 𝒪 E as a Z Γ -module. In particular we show that the fourth power of the (locally free) class of 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 ℰ E , together with new determinantal congruences for cyclic group rings and corresponding...

On the Galois structure of the square root of the codifferent

D. Burns (1991)

Journal de théorie des nombres de Bordeaux

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

Class groups of abelian fields, and the main conjecture

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 χ -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...