Displaying similar documents to “Asymptotics of number fields and the Cohen–Lenstra heuristics”

Steinitz classes of some abelian and nonabelian extensions of even degree

Alessandro Cobbe (2010)

Journal de Théorie des Nombres de Bordeaux

Similarity:

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

Similarity:

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.

Absolute norms of p -primary units

Supriya Pisolkar (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We prove a local analogue of a theorem of J. Martinet about the absolute norm of the relative discriminant ideal of an extension of number fields. The result can be seen as a statement about 2 -primary units. We also prove a similar statement about the absolute norms of p -primary units, for all primes p .

Note on the Galois module structure of quadratic extensions

Günter Lettl (1994)

Colloquium Mathematicae

Similarity:

In this note we will determine the associated order of relative extensions of algebraic number fields, which are cyclic of prime order p, assuming that the ground field is linearly disjoint to the pth cyclotomic field, ℚ ( p ) . For quadratic extensions we will furthermore characterize when the ring of integers of the extension field is free over the associated order. All our proofs are quite elementary. As an application, we will determine the Galois module structure of ℚ ( n ) / ℚ ( n ) + .