ON THE SCALED TRACE FORMS AND THE TRANSFER OF A NUMBER-FIELD EXTENSION

Let F be a number field. Let L F be a field extension of degree m and let Tr L F be the trace map. In this paper we ask for which quadratic forms φ{symbol} over F with dim φ{symbol} = mn does exist a form ρ{variant} over L with dim ρ{variant} = n such that φ{symbol} is isometric to Tr L F(ρ{variant}). We further show that for given m, n, r ∈ N and quadratic forms φ{symbol}1, ..., φ{symbol}r over F with dim φ{symbol}i = mn there exist an extension L F of degree m and ρ{variant}1, ..., ρ{variant}r over L with dim ρ{variant}i = n such that Tr L F(ρ{variant}i) is isometric to φ{symbol}i for i = 1, ..., r. © 1992.