Witt equivalence classes of quartic number fields

Abstract

It has recently been established that there are exactly seven Witt equivalence classes of quadratic number fields, and then all quadratic and cubic number fields have been classified with respect to Witt equivalence. In this paper we have classified number fields of degree four. Using this classification, we have proved the Conjecture of Szymiczek about the representability of Witt equivalence classes by quadratic extensions of quadratic fields.