The norm principle for type $D_n$ groups over complete discretely valued fields

Abstract

Let K be a complete discretely valued field with residue field k with char(k) = 2. Assuming that the norm principle holds for extended Clifford groups Ω(q) for every even dimensional non-degenerate quadratic form q defined over any finite extension of k, we show that it holds for extended Clifford groups Ω(Q) for every even dimensional nondegenerate quadratic form Q defined over K.