Badly approximable S-numbers and absolute Schmidt games

Abstract Let K be a number field, let S be the set of all normalized, non-conjugate Archimedean valuations of K , and let K S = ∏ v ∈ S K v be the Minkowski space associated with K . We strengthen recent results of [ESK10] and [EGL15] by showing that the set of badly approximable elements of K S is H -absolute winning for a certain family of subspaces of K S .