Displaying similar documents to “ p -divisible groups with complex multiplication over W ( k )

Group Schemes over artinian rings and Applications

Ioan Berbec (2009)

Annales de l’institut Fourier

Similarity:

Let n be a positive integer and A a complete characteristic zero discrete valuation ring with maximal ideal 𝔪 , absolute ramification index e < p - 1 and perfect residue field k of characteristic p > 2 . In this paper we classify smooth finite dimensional formal p - groups over A n = A / 𝔪 n A , groups on which the “multiplication by p ” morphism is faithfully flat, in particular p -divisible groups. As applications, we prove that p -divisible groups over k , and the morphisms between them, lift canonically to A / p A , and...

Ramification groups in Artin-Schreier-Witt extensions

Lara Thomas (2005)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let K be a local field of characteristic p > 0 . The aim of this paper is to describe the ramification groups for the pro- p abelian extensions over K with regards to the Artin-Schreier-Witt theory. We shall carry out this investigation entirely in the usual framework of local class field theory. This leads to a certain non-degenerate pairing that we shall define in detail, generalizing in this way the Schmid formula to Witt vectors of length n . Along the way, we recover a result of Brylinski...

On the classgroups of imaginary abelian fields

David Solomon (1990)

Annales de l'institut Fourier

Similarity:

Let p be an odd prime, χ an odd, p -adic Dirichlet character and K the cyclic imaginary extension of Q associated to χ . We define a “ χ -part” of the Sylow p -subgroup of the class group of K and prove a result relating its p -divisibility to that of the generalized Bernoulli number B 1 , χ - 1 . This uses the results of Mazur and Wiles in Iwasawa theory over Q . The more difficult case, in which p divides the order of χ is our chief concern. In this case the result is new and confirms an earlier conjecture...

Iwasawa theory for elliptic curves over imaginary quadratic fields

Massimo Bertolini (2001)

Journal de théorie des nombres de Bordeaux

Similarity:

Let E be an elliptic curve over , let K be an imaginary quadratic field, and let K be a p -extension of K . Given a set Σ of primes of K , containing the primes above p , and the primes of bad reduction for E , write K Σ for the maximal algebraic extension of K which is unramified outside Σ . This paper is devoted to the study of the structure of the cohomology groups H i ( K Σ / K , E p ) for i = 1 , 2 , and of the p -primary Selmer group Sel p ( E / K ) , viewed as discrete modules over the Iwasawa algebra of K / K . ...

Capitulation for even K -groups in the cyclotomic p -extension.

Romain Validire (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let p be a prime number and F be a number field. Since Iwasawa’s works, the behaviour of the p -part of the ideal class group in the p -extensions of F has been well understood. Moreover, M. Grandet and J.-F. Jaulent gave a precise result about its abelian p -group structure. On the other hand, the ideal class group of a number field may be identified with the torsion part of the K 0 of its ring of integers. The even K -groups of rings of integers appear as higher...