On extensions of the maximal cyclotomic field having a given classical Galois group.
On generalized Redei functions.
On linear dependence of roots
On normal binomials
On Solvability by Radicals of Field Extensions.
On Solvability by Radicals of Finite Fields.
On the congruence , where q is a prime and f is a k-normal polynomial
Orderings under field extensions.
-extensions abéliennes
Plongeants d'extensions galoisiennes
Plongement d'une extension diédrale dans une extension diédrale ou quaternionienne
On utilise les méthodes de Neukirch et Poitou pour écrire les conditions locales et globales des problèmes de plongement. Le cas étudié ici est celui du plongement d’une extension diédrale dans une extension diédrale ou quaternionienne, le corps de base étant un corps de nombres.
Polynomials of the form and pseudoprimes with respect to linear recurring sequences
Quadratic Forms Under Algebraic Extensions.
Relative Bogomolov extensions
A subfield K ⊆ ℚ̅ has the Bogomolov property if there exists a positive ε such that no non-torsion point of has absolute logarithmic height below ε. We define a relative extension L/K to be Bogomolov if this holds for points of . We construct various examples of extensions which are and are not Bogomolov. We prove a ramification criterion for this property, and use it to show that such extensions can always be constructed if some rational prime has bounded ramification index in K.
Sous-corps fermés du complété de la clôture algébrique d'un corps local.
Sous-corps fermés du complété de la clôture algébrique d'un corps local
Structure theorems for radical extensions of fields
Tamely ramified extensions's structure.
The effect on associated prime ideals produced by an extension of the base field.
The Galois group of generic symmetric matrices