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A note on the continuous extensions of injective morphisms between free groups to relatively fre profinite groups.

Thierry Coulbois, Mark Sapir, Pascal Weil (2003)

Publicacions Matemàtiques

Let V be a pseudovariety of finite groups such that free groups are residually V, and let φ: F(A) → F(B) be an injective morphism between finitely generated free groups. We characterize the situations where the continuous extension φ' of φ between the pro-V completions of F(A) and F(B) is also injective. In particular, if V is extension-closed, this is the case if and only if φ(F(A)) and its pro-V closure in F(B) have the same rank. We examine a number of situations where the injectivity of φ' can...

Bicyclic commutator quotients with one non-elementary component

Daniel Mayer (2023)

Mathematica Bohemica

For any number field K with non-elementary 3 -class group Cl 3 ( K ) ≃ C 3 e × C 3 , e ≥ 2 , the punctured capitulation type ϰ ( K ) of K in its unramified cyclic cubic extensions L i , 1 ≤ i ≤ 4 , is an orbit under the action of S 3 × S 3 . By means of Artin’s reciprocity law, the arithmetical invariant ϰ ( K ) is translated to the punctured transfer kernel type ϰ ( G 2 ) of the automorphism group G 2 = Gal ( F 3 2 ( K ) / K ) of the second Hilbert 3 -class field of K . A classification of finite 3 -groups G with low order and bicyclic commutator quotient G / G ' ≃ C 3 e × C 3 , 2 ≤ e ≤ 6 , according to the algebraic invariant...

Conjugacy classes of series in positive characteristic and Witt vectors.

Sandrine Jean (2009)

Journal de Théorie des Nombres de Bordeaux

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 by means...

Deformations and derived categories

Frauke M. Bleher, Ted Chinburg (2005)

Annales de l'institut Fourier

In this paper we generalize the deformation theory of representations of a profinite group developed by Schlessinger and Mazur to deformations of objects of the derived category of bounded complexes of pseudocompact modules for such a group. We show that such objects have versal deformations under certain natural conditions, and we find a sufficient condition for these versal deformations to be universal. Moreover, we consider applications to deforming Galois cohomology classes and the étale hypercohomology...

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