Displaying similar documents to “Capitulation for even K -groups in the cyclotomic ℤ p -extension.”

Steinitz classes of some abelian and nonabelian extensions of even degree

Alessandro Cobbe (2010)

Journal de Théorie des Nombres de Bordeaux

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The Steinitz class of a number field extension K / k is an ideal class in the ring of integers 𝒪 k of k , which, together with the degree [ K : k ] of the extension determines the 𝒪 k -module structure of 𝒪 K . We denote by R t ( k , G ) the set of classes which are Steinitz classes of a tamely ramified G -extension of k . We will say that those classes are realizable for the group G ; it is conjectured that the set of realizable classes is always a group. In this paper we will develop some of the ideas contained...

Bounds For Étale Capitulation Kernels II

Mohsen Asghari-Larimi, Abbas Movahhedi (2009)

Annales mathématiques Blaise Pascal

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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.

Selmer groups for elliptic curves in ℤ l d -extensions of function fields of characteristic p

Andrea Bandini, Ignazio Longhi (2009)

Annales de l’institut Fourier

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Let F be a function field of characteristic p > 0 , ℱ / F a ℤ l d -extension (for some prime l ≠ p ) and E / F a non-isotrivial elliptic curve. We study the behaviour of the r -parts of the Selmer groups ( r any prime) in the subextensions of ℱ via appropriate versions of Mazur’s Control Theorem. As a consequence we prove that the limit of the Selmer groups is a cofinitely generated (in some cases cotorsion) module over the Iwasawa algebra of ℱ / F .

Galois co-descent for étale wild kernels and capitulation

Manfred Kolster, Abbas Movahhedi (2000)

Annales de l'institut Fourier

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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...

Some remarks on almost rational torsion points

John Boxall, David Grant (2006)

Journal de Théorie des Nombres de Bordeaux

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For a commutative algebraic group G over a perfect field k , Ribet defined the set of almost rational torsion points G tors , k ar of G over k . For positive integers d , g , we show there is an integer U d , g such that for all tori T of dimension at most d over number fields of degree at most g , T tors , k ar ⊆ T [ U d , g ] . We show the corresponding result for abelian varieties with complex multiplication, and under an additional hypothesis, for elliptic curves without complex multiplication. Finally, we show that except for an explicit...