Okutsu invariants and Newton polygons
On 2-extensions of the rationals with restricted ramification
For a finite group G let 𝒦₂(G) denote the set of normal number fields (within ℂ) with Galois group G which are 2-ramified, that is, unramified outside {2,∞}. We describe the 2-groups G for which 𝒦₂(G) ≠ ∅, and determine the fields in 𝒦₂(G) for certain distinguished 2-groups G appearing (dihedral, semidihedral, modular and semimodular groups). Our approach is based on Fröhlich's theory of central field extensions, and makes use of ring class field constructions (complex multiplication).
On extensions of number fields obtained by specializing branched coverings.
On general local reciprocity maps.
On norm maps for one dimensional formal groups. II. ...-extensions of local fields with algebraically closed residue field.
On semicontinuity of ramification invariants in dimension 2.
On the cyclicity of a Galois module in local fields.
On the genus group of algebraic number fields
On the Iwasawa invariants of certain -extensions
On the jumps in the series of ramifications groups
On the main invariant of an element over a local field.
On the nonessential discriminant divisor of an algebraic number field
On the product formula in Galois groups.
On the ramification numbers of cyclic p-extensions over local fields.
On the ramification set of a positive quadratic form over an algebraic number field
On two types of complete discrete valuation fields
On Unramified Galois Extensions Over Maximum Abelian Extensions of Algebraic Number Fields.
Optimisation du théorème d’Ax-Sen-Tate et application à un calcul de cohomologie galoisienne -adique
Soit un corps -adique, son groupe de Galois absolu et la valuation sur . Dans sa démonstration du théorème d’Ax-Sen-Tate, Ax montre que si pour un , vérifie pour tout , alors il existe tel que , avec . Ax se pose la question de l’optimalité de la constante , que nous étudions ici. En utilisant l’extension de engendrée par les racines -es d’une uniformisante fixée de , nous déterminons la constante optimale, ainsi que des informations supplémentaires sur les tels que pour...
Orthogonal representations of Galois groups, Stiefel-Whitney classes and Hasse-Witt invariants.