Add to ORKGInternational audienceWe study the distribution of extensions of a number field $k$ with fixed abelian Galois group $G$, from which a given finite set of elements of $k$ are norms. In particular, we show the existence of such extensions. Along the way, we show that the Hasse norm principle holds for $100\%$ of $G$-extensions of $k$, when ordered by conductor. The appendix contains an alternative purely geometric proof of our existence result
A classical result of Hasse states that the norm principle holds for finite cyclic extensions of glo...
For a finite group $G$, we introduce a generalization of norm relations in the group algebra $\mathb...
International audienceFor a finite group $G$, we introduce a generalization of norm relations in the...
International audienceWe study the distribution of extensions of a number field $k$ with fixed abeli...
We study the distribution of extensions of a number field $k$ with fixed abelian Galois group $G$, f...
We study the distribution of extensions of a number field k with fixed abelian Galois group G, from ...
We study the distribution of extensions of a number field $k$ with fixed abelian Galois group $G$, f...
AbstractOne of the fundamental theorems of global class field theory states that there is a one-to-o...
We study the distribution of abelian extensions of bounded discriminant of a number field $k$ which ...
We study the distribution of abelian extensions of bounded discriminant of a number field k which fa...
AbstractLet E/k be a Galois extension of algebraic number fields with the Galois group isomorphic to...
AbstractLetL/kandT/kbe finite extensions of algebraic number fields. In the present work we introduc...
AbstractWe propose a conjecture on the distribution of number fields with given Galois group and bou...
Let F be a finite extension field of Qp, A an abelian variety defined over F with ordinary good redu...
We show that under certain conditions a rational number is a norm in a given finite Galois extension...
A classical result of Hasse states that the norm principle holds for finite cyclic extensions of glo...
For a finite group $G$, we introduce a generalization of norm relations in the group algebra $\mathb...
International audienceFor a finite group $G$, we introduce a generalization of norm relations in the...
International audienceWe study the distribution of extensions of a number field $k$ with fixed abeli...
We study the distribution of extensions of a number field $k$ with fixed abelian Galois group $G$, f...
We study the distribution of extensions of a number field k with fixed abelian Galois group G, from ...
We study the distribution of extensions of a number field $k$ with fixed abelian Galois group $G$, f...
AbstractOne of the fundamental theorems of global class field theory states that there is a one-to-o...
We study the distribution of abelian extensions of bounded discriminant of a number field $k$ which ...
We study the distribution of abelian extensions of bounded discriminant of a number field k which fa...
AbstractLet E/k be a Galois extension of algebraic number fields with the Galois group isomorphic to...
AbstractLetL/kandT/kbe finite extensions of algebraic number fields. In the present work we introduc...
AbstractWe propose a conjecture on the distribution of number fields with given Galois group and bou...
Let F be a finite extension field of Qp, A an abelian variety defined over F with ordinary good redu...
We show that under certain conditions a rational number is a norm in a given finite Galois extension...
A classical result of Hasse states that the norm principle holds for finite cyclic extensions of glo...
For a finite group $G$, we introduce a generalization of norm relations in the group algebra $\mathb...
International audienceFor a finite group $G$, we introduce a generalization of norm relations in the...