Displaying similar documents to “Wintenberger’s functor for abelian extensions”

On the trace of the ring of integers of an abelian number field

Kurt Girstmair (1992)

Acta Arithmetica

Similarity:

Let K, L be algebraic number fields with K ⊆ L, and O K , O L their respective rings of integers. We consider the trace map T = T L / K : L K and the O K -ideal T ( O L ) O K . By I(L/K) we denote the group indexof T ( O L ) in O K (i.e., the norm of T ( O L ) over ℚ). It seems to be difficult to determine I(L/K) in the general case. If K and L are absolutely abelian number fields, however, we obtain a fairly explicit description of the number I(L/K). This is a consequence of our description of the Galois module structure of T ( O L ) (Theorem 1)....

Representation of finite abelian group elements by subsequence sums

David J. Grynkiewicz, Luz E. Marchan, Oscar Ordaz (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let G C n 1 ... C n r be a finite and nontrivial abelian group with n 1 | n 2 | ... | n r . A conjecture of Hamidoune says that if W = w 1 · ... · w n is a sequence of integers, all but at most one relatively prime to | G | , and S is a sequence over G with | S | | W | + | G | - 1 | G | + 1 , the maximum multiplicity of S at most | W | , and σ ( W ) 0 mod | G | , then there exists a nontrivial subgroup H such that every element g H can be represented as a weighted subsequence sum of the form g = n i = 1 w i s i , with s 1 · ... · s n a subsequence of S . We give two examples showing this does not hold in general, and characterize the...

Constructing class fields over local fields

Sebastian Pauli (2006)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let K be a 𝔭 -adic field. We give an explicit characterization of the abelian extensions of K of degree p by relating the coefficients of the generating polynomials of extensions L / K of degree p to the exponents of generators of the norm group N L / K ( L * ) . This is applied in an algorithm for the construction of class fields of degree p m , which yields an algorithm for the computation of class fields in general.

Conjugacy classes of series in positive characteristic and Witt vectors.

Sandrine Jean (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let k be the algebraic closure of 𝔽 p and K be the local field of formal power series with coefficients in k . The aim of this paper is the description of the set 𝒴 n of conjugacy classes of series of order p n for the composition law. This work is concerned with the formal power series with coefficients in a field of characteristic p which are invertible and of finite order p n for the composition law. In order to investigate Oort’s conjecture, I give a description of conjugacy classes of series...

The integral logarithm in Iwasawa theory : an exercise

Jürgen Ritter, Alfred Weiss (2010)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let l be an odd prime number and H a finite abelian l -group. We describe the unit group of Λ [ H ] (the completion of the localization at l of l [ [ T ] ] [ H ] ) as well as the kernel and cokernel of the integral logarithm L : Λ [ H ] × Λ [ H ] , which appears in non-commutative Iwasawa theory.

On a dynamical Brauer–Manin obstruction

Liang-Chung Hsia, Joseph Silverman (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let ϕ : X X be a morphism of a variety defined over a number field  K , let  V X be a K -subvariety, and let  𝒪 ϕ ( P ) = { ϕ n ( P ) : n 0 } be the orbit of a point  P X ( K ) . We describe a local-global principle for the intersection  V 𝒪 ϕ ( P ) . This principle may be viewed as a dynamical analog of the Brauer–Manin obstruction. We show that the rational points of  V ( K ) are Brauer–Manin unobstructed for power maps on  2 in two cases: (1)  V is a translate of a torus. (2)  V is a line and  P has a preperiodic coordinate. A key tool in the proofs is the...