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Sur le 2 -groupe de classes des corps multiquadratiques réels

Ali MouhibAbbas Movahhedi — 2005

Journal de Théorie des Nombres de Bordeaux

Soient p 1 , p 2 , . . . , p n des nombres premiers distincts - 1 ( m o d 4 ) , d : = p 1 p 2 p n et k n = Q ( p 1 , p 2 , . . . , p n ) . On peut approcher le 2 -rang du groupe de classes des corps k n en étudiant celui du corps k m ( d ) pour un entier m < n . Dans cet article, on traite le cas où m = 2 ou 3 . Comme application, on déduit que le rang du 2 -groupe de classes de k 4 est au moins égal à deux (on savait déjà grâce à un résultat de Fröhlich que le groupe de classes de k 4 est toujours d’ordre pair). On en déduit également la liste de tous les corps multiquadratiques k n ayant un 2 -groupe de classes...

Galois co-descent for étale wild kernels and capitulation

Manfred KolsterAbbas Movahhedi — 2000

Annales de l'institut Fourier

Let F be a number field with ring of integers o F . For a fixed prime number p and i 2 the étale wild kernels W K 2 i - 2 e ´ t ( F ) are defined as kernels of certain localization maps on the i -fold twist of the p -adic étale cohomology groups of spec o F [ 1 p ] . These groups are finite and coincide for i = 2 with the p -part of the classical wild kernel W K 2 ( F ) . They play a role similar to the p -part of the p -class group of F . For class groups, Galois co-descent in a cyclic extension L / F is described by the ambiguous class formula given by genus theory....

Bounds For Étale Capitulation Kernels II

Mohsen Asghari-LarimiAbbas Movahhedi — 2009

Annales mathématiques Blaise Pascal

Let p be an odd prime and E / F a cyclic p -extension of number fields. We give a lower bound for the order of the kernel and cokernel of the natural extension map between the even étale K -groups of the ring of S -integers of E / F , where S is a finite set of primes containing those which are p -adic.

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