Resumen de Classes de steinitz et extensions quaternioniennes

Richard Massy, Bouchaib Sodaïgui

• Let k be a number field. We prove that the set of Steinitz clases of quadratic extensions K/ k which can be embedded in quaternionic extensions of degree 8, tamely or wildly ramified over k, is the full class group Cl(k) of k. Moreover, we provide explicit formulas to construct these quaternionic extensions.