Our basic representation of the data is a Galois lattice, i.e. a lattice in which the terms of a representation language are partitioned into equivalence classes w.r.t. their extent (the extent of a term is the part of the instance set that satisfies the term). We propose here to simplify our view of the data, still conserving the Galois lattice formal structure. For that purpose we use a preli...

Let L be a Galois extension of K, fields, with Galois group Γ. We obtain two results. First, if Γ = Hol(Zpe ), we determine the number of Hopf Galois structures on L/K where the associated group of the Hopf algebra H is Γ (i.e. L⊗K H ∼= L[Γ]). Now let p be a safeprime, that is, p is a prime such that q = (p−1)/2 > 2 is also prime. If L/K is Galois with group Γ = Hol(Zp), p a safeprime, then for...

Let F/k be a Galois extension of number fields with dihedral Galois group of order 2q, where q is an odd integer. We express a certain quotient of S -class numbers of intermediate fields, arising from Brauer-Kuroda relations, as a unit index. Our formula is valid for arbitrary extensions with Galois group D2q and for arbitrary Galois-stable sets of primes S , containing the Archimedean ones. Ou...

We describe a locally trivial quantum principal U (1)-bundle over the quantum space S 2 pq which is a noncommutative analogue of the usual Hopf bundle. We also provide results concerning the structure of its total space algebra (irreducible *-representations and topological K-groups) and its Galois aspects (Galois property, existence of a strong connection, non-cleftness).

This paper introduces a new approach to the study of certain aspects of Galois module theory by combining ideas arising from the study of the Galois structure of torsors of finite group schemes with techniques coming from relative algebraic K-theory.

Fix K a p-adic field and denote by GK its absolute Galois group. Let K∞ be the extension of K obtained by adding p-th roots of a fixed uniformizer, and G∞ ⊂ GK its absolute Galois group. In this article, we define a class of p-adic torsion representations of G∞, named quasi-semi-stable. We prove that these representations are “explicitly” described by a certain category of linear algebra object...

— We study the structure of abelian subgroups of Galois groups of function fields of surfaces.

— We study the structure of abelian subgroups of Galois groups of function fields of surfaces.

Much work has gone into matrix representations of Galois groups, but there is a whole new class of naturally occurring representations that have as yet gone almost unnoticed. In fact, it is well-known in various areas of mathematics that the main sources of totally disconnected groups are matrix groups over local fields AND automorphism groups of locally finite trees [12]. It is perhaps surpris...