Some results about number fields with Polya groups equal to ideal class groups

The Polya group of a number field K is a specific subgroup of the ideal class group Cl(K) of K, generated by all classes of Ostrowski ideals of K. In this talk, I will discuss the equality Po(K)=Cl(K) in two directions. First, we will see this equality happens for infinitely many "non-Galois fields'' K. Accordingly, I prove two conjectures presented by Chabert and Halberstadt concerning the Polya groups of some families of non-Galois fields. Then, I present some "finiteness theorems" for the equality Po(K)=Cl(K) for some families of "Galois" fields K obtained in joint work with Amir Akbary (University of Lethbridge).