6 problems

Let $L/K$ be a weakly ramified Galois extension of number fields of odd degree. Write $\mathfrak{a}_{L/K}$ for the canonical pre-image associated with the stable-isomorphism class…

Let $K$ be a number field. Call $K$ a Leopoldt field if every tame abelian extension $L/K$ has a weak normal integral basis, meaning that, for the maximal order $\mathcal{M}$ of…

Let $F_{\pi}/F$ be a finite Galois-algebra extension of number fields with group $G$. Write $\mathfrak{D}(\pi)$ for its different, and suppose that the square root $A(\pi)$ of…

Fröhlich's conjecture. The class of $\mathcal{O}_E$ in the locally free class group of $\mathbb{Z}[G]$ is determined by the Artin root numbers associated to the irreducible complex…

Let $K$ be a number field and let $G$ be a finite abelian group. For a $G$-Galois extension $L/K$, let $\mathcal{A}_{L/K}$ be the associated order and let … be the adjusted ring of…

HS-L$(K,G)$ conjecture. $K$ is a Hilbert-Speiser field of type $G$ if and only if $K$ is a Leopoldt field of type $G$. This generalizes the equivalence of the unrestricted Hilbert-…