Tame kernels of cyclic extensions of number fields
The Brauer-Kuroda formula for higher S-class numbers in dihedral extensions of number fields
The cyclic subfield integer index
In this note we consider the index in the ring of integers of an abelian extension of a number field of the additive subgroup generated by integers which lie in subfields that are cyclic over . This index is finite, it only depends on the Galois group and the degree of , and we give an explicit combinatorial formula for it. When generalizing to more general Dedekind domains, a correction term can be needed if there is an inseparable extension of residue fields. We identify this correction term...
The distribution of second -class groups on coclass graphs
General concepts and strategies are developed for identifying the isomorphism type of the second -class group , that is the Galois group of the second Hilbert -class field , of a number field , for a prime . The isomorphism type determines the position of on one of the coclass graphs , , in the sense of Eick, Leedham-Green, and Newman. It is shown that, for special types of the base field and of its -class group , the position of is restricted to certain admissible branches of coclass...
The Divisibility of Normal Integral Generators.
The field descent and class groups of CM-fields
The Galois Group of a Radical Extension of the Rationals.
The Hasse conjecture for cyclic extensions.
The imaginary cyclic sextic fields with class numbers equal to their genus class numbers
It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic sextic fields with class numbers equal to their genus class numbers.
The narrow class groups of some ℤₚ-extensions over the rationals
The ring of integers of an abelian number field.
Tours de Hilbert des extensions cubiques cycliques de Q.
Trivialité du -rang du noyau hilbertien
We give exhaustive list of biquadratic fields and without -exotic symbol, i.e. for which the -rank of the Hilbert kernel (or wild kernel) is zero. Such are logarithmic principals [J3]. We detail an exemple of this technical numerical exploration and quote the family of theories and results we utilize. The -rank of tame, regular and wild kernel of -theory are connected with local and global problem of embedding in a -extension. Global class field theory can describe the -rank of the Hilbert...