Relations d'inégalités effectives en théorie algébrique des nombres
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.
Relative integral basis for algebraic number fields.
Remark on a problem of Schinzel
Representation of a prime as the sum of squares in a tower of fields.
Réseaux sur les anneaux d'entiers algébriques
Résidus de puissances
Résultats de stabilité algébrique.
Résultats récents sur la monogénéité des anneaux d' entiers
Roots of unity in definite quaternion orders
A commutative order in a quaternion algebra is called selective if it embeds into some, but not all, of the maximal orders in the algebra. It is known that a given quadratic order over a number field can be selective in at most one indefinite quaternion algebra. Here we prove that the order generated by a cubic root of unity is selective for any definite quaternion algebra over the rationals with type number 3 or larger. The proof extends to a few other closely related orders.
Rotations sur les groupes, nombres algébriques, et substitutions