Christopher Frei (Graz): Constructing Abelian extensions with prescribed norms

Austrian-Hungarian Diophantine Number Theory seminar
https://uni-salzburg.webex.com/uni-salzburg/j.php?MTID=mac8f69c96c99d70601ce8e57e854e266

Abstract: Let _K_ be a number field, _S_ a finite set of elements of _K_, and _ G_ a finite abelian group. We explain how to
construct explicitly a normal extension _L_ of _K_ with Galois group _G_, such that all elements of _S_ are norms of elements
of _L_. The construction is based on class field theory and a recent formulation of Tate's criterion for the validity of the
Hasse norm principle. This is joint work with Rodolphe Richard (UCL).